Journal of the London Mathematical Society-Second Series最新文献

{"title":"The first Steklov eigenvalue of planar graphs and beyond","authors":"Huiqiu Lin,  Da Zhao","doi":"10.1112/jlms.70238","DOIUrl":"10.1112/jlms.70238","url":null,"abstract":"<p>The Steklov eigenvalue problem was introduced over a century ago, and its discrete form attracted interest recently. Let <span></span><math>\u0000 <semantics>\u0000 <mi>D</mi>\u0000 <annotation>$D$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>δ</mi>\u0000 <mi>Ω</mi>\u0000 </mrow>\u0000 <annotation>$delta Omega$</annotation>\u0000 </semantics></math> be the maximum vertex degree and the set of vertices of degree one in a graph <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$mathcal {G}$</annotation>\u0000 </semantics></math>, respectively. Let <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <annotation>$lambda _2$</annotation>\u0000 </semantics></math> be the first (non-trivial) Steklov eigenvalue of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>G</mi>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 <mi>Ω</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(mathcal {G}, delta Omega)$</annotation>\u0000 </semantics></math>. In this paper, using the circle packing theorem and conformal mapping, we first show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo>⩽</mo>\u0000 <mn>8</mn>\u0000 <mi>D</mi>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>δ</mi>\u0000 <mi>Ω</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$lambda _2 leqslant 8D / |delta Omega |$</annotation>\u0000 </semantics></math> for planar graphs. This can be seen as a discrete analog of Kokarev's bound, that is, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>λ</mi>\u0000 <mn>2</mn>\u0000 </msub>\u0000 <mo><</mo>\u0000 <mn>8</mn>\u0000 <mi>π</mi>\u0000 <mo>/</mo>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>∂</mi>\u0000 <mi>Ω</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$lambda _2 < 8pi / |partial Omega |$</annotation>\u0000 </semantics></math> for compact surfaces with boundary of genus 0. Let <span></span><math>\u0000 <semantics>\u0000 <mi>B</mi>\u0000 <annotation>$B$</annotation>\u0000 </semantics></ma","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144647282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Subgroups of word hyperbolic groups in dimension 2 over arbitrary rings","authors":"Shaked Bader,&nbsp;Robert Kropholler,&nbsp;Vladimir Vankov","doi":"10.1112/jlms.70230","DOIUrl":"10.1112/jlms.70230","url":null,"abstract":"<p>In 1996, Gersten proved that finitely presented subgroups of a word hyperbolic group of integral cohomological dimension 2 are hyperbolic. We use isoperimetric functions over arbitrary rings to extend this result to any ring. In particular, we study the discrete isoperimetric function and show that its linearity is equivalent to hyperbolicity, which is also equivalent to it being subquadratic. We further use these ideas to obtain conditions for subgroups of higher rank hyperbolic groups to be again higher rank hyperbolic of the same rank. The appendix discusses the equivalence between isoperimetric functions and coning inequalities in the simplicial setting and the general setting, leading to combinatorial definitions of higher rank hyperbolicity in the setting of simplicial complexes and allowing us to give elementary definitions of higher rank hyperbolic groups.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70230","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144615313","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Structural stability of cylindrical supersonic solutions to the steady Euler–Poisson system","authors":"Chunpeng Wang,&nbsp;Zihao Zhang","doi":"10.1112/jlms.70229","DOIUrl":"10.1112/jlms.70229","url":null,"abstract":"<p>This paper concerns the structural stability of smooth cylindrically symmetric supersonic Euler–Poisson flows in nozzles. Both three-dimensional and axisymmetric perturbations are considered. On one hand, we establish the existence and uniqueness of three-dimensional smooth supersonic solutions to the potential flow model of the steady Euler–Poisson system. On the other hand, the existence and uniqueness of smooth supersonic flows with nonzero vorticity to the steady axisymmetric Euler–Poisson system are proved. The problem is reduced to solve a nonlinear boundary value problem for a hyperbolic–elliptic mixed system. One of the key ingredients in the analysis of three-dimensional supersonic irrotational flows is the well-posedness theory for a linear second-order hyperbolic–elliptic coupled system, which is achieved by using the multiplier method and the reflection technique to derive the energy estimates. For smooth axisymmetric supersonic flows with nonzero vorticity, the deformation-curl-Poisson decomposition is utilized to reformulate the steady axisymmetric Euler–Poisson system as a deformation-curl-Poisson system together with several transport equations, so that one can design a two-layer iteration scheme to establish the nonlinear structural stability of the background supersonic flow within the class of axisymmetric rotational flows.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144624283","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Toric wedge induction and toric lifting property for piecewise linear spheres with few vertices","authors":"Suyoung Choi,&nbsp;Hyeontae Jang,&nbsp;Mathieu Vallée","doi":"10.1112/jlms.70231","DOIUrl":"10.1112/jlms.70231","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;annotation&gt;$K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be an &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(n-1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional piecewise linear sphere on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;[&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;]&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$[m]$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;⩽&lt;/mo&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mn&gt;4&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mleqslant n+4$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. There are a canonical action of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;annotation&gt;$m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-dimensional torus &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;T&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$T^m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on the moment-angle complex &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathcal {Z}_K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and a canonical action of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$mathbb {Z}_2^m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on the real moment-angle complex &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mi&gt;K&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathbb {R}mathcal {Z}_K$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$mathbb {Z}_2$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the additive group with two elements. We prove that any subgroup of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$mathbb {Z}_2^m$&lt;/annotation&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144611997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simply connected positive Sasakian 5-manifolds","authors":"Dasol Jeong,&nbsp;Jihun Park,&nbsp;Joonyeong Won","doi":"10.1112/jlms.70227","DOIUrl":"10.1112/jlms.70227","url":null,"abstract":"<p>We investigate closed simply connected 5-manifolds capable of hosting positive Sasakian structures. We present a conjectural comprehensive list of such manifolds.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70227","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144611998","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the global existence for the modified Camassa–Holm equation","authors":"Yiling Yang,&nbsp;Engui Fan,&nbsp;Yue Liu","doi":"10.1112/jlms.70232","DOIUrl":"10.1112/jlms.70232","url":null,"abstract":"<p>The modified Camassa–Holm (mCH) equation is a model to describe the unidirectional propagation of shallow water waves. Without knowledge of any conservation quantities in the higher order Sobolev spaces for this type of the quasi-linear evaluation equation, obtaining global well-posedness for the mCH equation appears to be quite challenging. In this paper, we address the existence of global solutions in a weighted Sobolev space <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msup>\u0000 <mi>H</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>R</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$H^{2,1}(mathbb {R})$</annotation>\u0000 </semantics></math> to the Cauchy problem for the mCH equation. The key to prove this result is establish bijectivity between potential and reflection coefficient by using inverse scattering transform method based on the Riemann–Hilbert problem associated with the Cauchy problem for the mCH equation.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144582205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On two-generator subgroups of mapping torus groups","authors":"Naomi Andrew,&nbsp;Edgar A. Bering IV,&nbsp;Ilya Kapovich,&nbsp;Stefano Vidussi,&nbsp;Peter Shalen","doi":"10.1112/jlms.70226","DOIUrl":"10.1112/jlms.70226","url":null,"abstract":"&lt;p&gt;We prove that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;⟨&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mo&gt;|&lt;/mo&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;⟩&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$G_varphi =langle F, t| t x t^{-1} =varphi (x), xin Frangle$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is the mapping torus group of an injective endomorphism &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$varphi: Frightarrow F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of a free group &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;annotation&gt;$F$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (of possibly infinite rank), then every two-generator subgroup &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;annotation&gt;$H$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$G_varphi$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is either free or a (finitary) sub-mapping torus. As an application we show that if &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mtext&gt;Out&lt;/mtext&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;F&lt;/mi&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$varphi in mbox{Out}(F_r)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a fully irreducible atoroidal automorphism, then every two-generator subgroup of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;G&lt;/mi&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144582101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Operator–Lipschitz functions on symmetrically normed ideals with nontrivial Boyd indices","authors":"E. Kissin,&nbsp;D. Potapov,&nbsp;V. Shulman,&nbsp;F. Sukochev","doi":"10.1112/jlms.70218","DOIUrl":"10.1112/jlms.70218","url":null,"abstract":"&lt;p&gt;We show that if the Boyd indices of a symmetrically normed ideal &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;annotation&gt;$J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$B(H)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; are nontrivial (differ from 1 and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;annotation&gt;$infty$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;), then for any Lipschitz function &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;annotation&gt;$f$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {C}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, the map &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;↦&lt;/mo&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Nmapsto f(N)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is Lipschitz on the set of normal operators with respect to the norm &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;mo&gt;·&lt;/mo&gt;\u0000 &lt;mo&gt;∥&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$Vert cdot Vert _{J}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. In particular, we study ideals for which some enhanced forms of the Fuglede Theorem hold; this is necessary for the work with functions of normal operators. We also consider functions that have the property of &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;annotation&gt;$J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-stability with respect to an ideal &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;annotation&gt;$J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;: if a normal operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;annotation&gt;$N$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is perturbed by an operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;J&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$Xin J$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; in such a way that the operator &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144573612","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dimension of homogeneous iterated function systems with algebraic translations","authors":"De-Jun Feng,&nbsp;Zhou Feng","doi":"10.1112/jlms.70222","DOIUrl":"10.1112/jlms.70222","url":null,"abstract":"&lt;p&gt;Let &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;annotation&gt;$ mu$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; be the self-similar measure associated with a homogeneous iterated function system &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;Φ&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ Phi = lbrace lambda x + t_j rbrace _{j=1}^m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; on &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;annotation&gt;$mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and a probability vector &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;annotation&gt;$ (p_{j})_{j=1}^m$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;0&lt;/mn&gt;\u0000 &lt;mo&gt;≠&lt;/mo&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0ne lambda in (-1,1)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$t_jin mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Recently by","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70222","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144551013","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Simple supercuspidal \u0000 \u0000 L\u0000 $L$\u0000 -packets of split special orthogonal groups over dyadic fields","authors":"Moshe Adrian,&nbsp;Guy Henniart,&nbsp;Eyal Kaplan,&nbsp;Masao Oi","doi":"10.1112/jlms.70223","DOIUrl":"10.1112/jlms.70223","url":null,"abstract":"<p>We consider the split special orthogonal group <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>SO</mo>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <annotation>$operatorname{SO}_{N}$</annotation>\u0000 </semantics></math> defined over a <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-adic field. We determine the structure of any <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-packet of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mo>SO</mo>\u0000 <mi>N</mi>\u0000 </msub>\u0000 <annotation>$operatorname{SO}_{N}$</annotation>\u0000 </semantics></math> containing a simple supercuspidal representation (in the sense of Gross–Reeder). We also determine its endoscopic lift to a general linear group. Combined with the explicit local Langlands correspondence for simple supercuspidal representations of general linear groups, this leads us to get an explicit description of the <span></span><math>\u0000 <semantics>\u0000 <mi>L</mi>\u0000 <annotation>$L$</annotation>\u0000 </semantics></math>-parameter as a representation of the Weil group of <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>. Our result is new when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$p=2$</annotation>\u0000 </semantics></math> and our method provides a new proof even when <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>≠</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$pne 2$</annotation>\u0000 </semantics></math>.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"112 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144524870","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}