Bulletin of the London Mathematical Society最新文献

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Inhomogeneous Khintchine–Groshev theorem without monotonicity 无单调性非齐次Khintchine-Groshev定理
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-06-04 DOI: 10.1112/blms.70114
Seongmin Kim
{"title":"Inhomogeneous Khintchine–Groshev theorem without monotonicity","authors":"Seongmin Kim","doi":"10.1112/blms.70114","DOIUrl":"10.1112/blms.70114","url":null,"abstract":"<p>The Khintchine–Groshev theorem in Diophantine approximation theory says that there is a dichotomy of the Lebesgue measure of sets of <span></span><math>\u0000 <semantics>\u0000 <mi>ψ</mi>\u0000 <annotation>$psi$</annotation>\u0000 </semantics></math>-approximable numbers, given a monotonic function <span></span><math>\u0000 <semantics>\u0000 <mi>ψ</mi>\u0000 <annotation>$psi$</annotation>\u0000 </semantics></math>. Allen and Ramírez removed the monotonicity condition from the inhomogeneous Khintchine–Groshev theorem for cases with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mi>m</mi>\u0000 <mo>⩾</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$nmgeqslant 3$</annotation>\u0000 </semantics></math> and conjectured that it also holds for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mi>m</mi>\u0000 <mo>=</mo>\u0000 <mn>2</mn>\u0000 </mrow>\u0000 <annotation>$nm=2$</annotation>\u0000 </semantics></math>. In this paper, we prove this conjecture in the case of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mo>(</mo>\u0000 <mn>2</mn>\u0000 <mo>,</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n,m)=(2,1)$</annotation>\u0000 </semantics></math>. We also prove it for the case of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>,</mo>\u0000 <mi>m</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mn>2</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(n,m)=(1,2)$</annotation>\u0000 </semantics></math> with a rational inhomogeneous parameter.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2639-2657"},"PeriodicalIF":0.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70114","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145021917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On profinite groups with the Magnus Property 在无限群上用Magnus属性
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-06-04 DOI: 10.1112/blms.70107
Claude Marion, Pavel Zalesskii
{"title":"On profinite groups with the Magnus Property","authors":"Claude Marion,&nbsp;Pavel Zalesskii","doi":"10.1112/blms.70107","DOIUrl":"10.1112/blms.70107","url":null,"abstract":"<p>A group is said to have the Magnus Property (MP) if whenever two elements have the same normal closure then they are conjugate or inverse-conjugate. We show that a profinite MP group <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is prosolvable and any quotient of it is again MP. As corollaries, we obtain that a prime divisor of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>|</mo>\u0000 <mi>G</mi>\u0000 <mo>|</mo>\u0000 </mrow>\u0000 <annotation>$|G|$</annotation>\u0000 </semantics></math> is 2, 3, 5 or 7, and the second derived subgroup of <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is pronilpotent. We also show that the inverse limit of an inverse system of profinite MP groups is again MP. Finally when <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> is finitely generated, we establish that <span></span><math>\u0000 <semantics>\u0000 <mi>G</mi>\u0000 <annotation>$G$</annotation>\u0000 </semantics></math> must in fact be finite.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2489-2497"},"PeriodicalIF":0.9,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Area estimates for capillary cmc hypersurfaces with nonpositive Yamabe invariant 非正Yamabe不变量毛细管cmc超曲面的面积估计
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-06-03 DOI: 10.1112/blms.70118
Leandro F. Pessoa, Erisvaldo Véras, Bruno Vieira
{"title":"Area estimates for capillary cmc hypersurfaces with nonpositive Yamabe invariant","authors":"Leandro F. Pessoa,&nbsp;Erisvaldo Véras,&nbsp;Bruno Vieira","doi":"10.1112/blms.70118","DOIUrl":"10.1112/blms.70118","url":null,"abstract":"&lt;p&gt;We prove area estimates for stable capillary &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mi&gt;c&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$cmc$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (minimal) hypersurfaces &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with nonpositive Yamabe invariant that are properly immersed in a Riemannian &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;-dimensional manifold &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; with scalar curvature &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$R^M$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and mean curvature of the boundary &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;H&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;∂&lt;/mi&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;annotation&gt;$H^{partial M}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; bounded from below. We also prove a local rigidity result in the case &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is embedded and &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;$mathcal {J}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-energy-minimizing. In this case, we show that &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; locally splits along &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;Σ&lt;/mi&gt;\u0000 &lt;annotation&gt;$Sigma$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and is isometric to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mi&gt;ε&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;ε&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;Σ&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;t&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;+&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;e&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;−&lt;/mo&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;mi&gt;H&lt;/m","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 9","pages":"2708-2722"},"PeriodicalIF":0.9,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145022116","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Skew odd orthogonal characters and interpolating Schur polynomials 偏奇正交特征和插值舒尔多项式
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-06-02 DOI: 10.1112/blms.70109
Naihuan Jing, Zhijun Li, Xinyu Pan, Danxia Wang, Chang Ye
{"title":"Skew odd orthogonal characters and interpolating Schur polynomials","authors":"Naihuan Jing,&nbsp;Zhijun Li,&nbsp;Xinyu Pan,&nbsp;Danxia Wang,&nbsp;Chang Ye","doi":"10.1112/blms.70109","DOIUrl":"10.1112/blms.70109","url":null,"abstract":"&lt;p&gt;We introduce two vertex operators to realize skew odd orthogonal characters &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;±&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$so_{lambda /mu }(mathbf {x}^{pm })$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; and derive the Cauchy identity for the skew characters via the Toeplitz–Hankel-type determinant as an analog of Schur functions. The method also gives new proofs of the Jacobi–Trudi identity and Gelfand–Tsetlin patterns for &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;s&lt;/mi&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;o&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;λ&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;mi&gt;μ&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mo&gt;±&lt;/mo&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$so_{lambda /mu }(mathbf {x}^{pm })$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;. Moreover, combining the vertex operators related to characters of types &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;D&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$C,D$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (Baker, &lt;i&gt;J. Phys. A&lt;/i&gt;. &lt;b&gt;29&lt;/b&gt;(12) (1996), 3099–3117; Jing and Nie, &lt;i&gt;Ann. Combin&lt;/i&gt;. &lt;b&gt;19&lt;/b&gt; (2015), 427–442) and the new vertex operators related to &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;annotation&gt;$B$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-type characters, we obtain three families of symmetric polynomials that interpolate among characters of &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;SO&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&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;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;C&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2509-2530"},"PeriodicalIF":0.9,"publicationDate":"2025-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814923","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On Poincaré polynomials for plane curves with quasi-homogeneous singularities 拟齐次奇异平面曲线的poincarcarr多项式
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-30 DOI: 10.1112/blms.70112
Piotr Pokora
{"title":"On Poincaré polynomials for plane curves with quasi-homogeneous singularities","authors":"Piotr Pokora","doi":"10.1112/blms.70112","DOIUrl":"10.1112/blms.70112","url":null,"abstract":"<p>We define a combinatorial object that can be associated with any conic-line arrangement with ordinary singularities, which we call the combinatorial Poincaré polynomial. We prove a Terao-type factorization statement on the splitting of such a polynomial over the rationals under the assumption that our conic-line arrangements are free and admit ordinary quasi-homogeneous singularities. Then we focus on the so-called <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-arrangements in the plane. In particular, we provide a combinatorial constraint for free <span></span><math>\u0000 <semantics>\u0000 <mi>d</mi>\u0000 <annotation>$d$</annotation>\u0000 </semantics></math>-arrangements admitting ordinary quasi-homogeneous singularities.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2549-2560"},"PeriodicalIF":0.9,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815220","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Construction of a curved Kakeya set 一个弯曲的Kakeya集合的构造
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-30 DOI: 10.1112/blms.70110
Tongou Yang, Yue Zhong
{"title":"Construction of a curved Kakeya set","authors":"Tongou Yang,&nbsp;Yue Zhong","doi":"10.1112/blms.70110","DOIUrl":"10.1112/blms.70110","url":null,"abstract":"<p>We construct a compact set in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>R</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$mathbb {R}^2$</annotation>\u0000 </semantics></math> of measure 0 containing a piece of a parabola of every aperture between 1 and 2. As a consequence, we improve lower bounds for the <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$L^p$</annotation>\u0000 </semantics></math>-<span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>L</mi>\u0000 <mi>q</mi>\u0000 </msup>\u0000 <annotation>$L^q$</annotation>\u0000 </semantics></math> norm of the corresponding maximal operator for a range of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>,</mo>\u0000 <mi>q</mi>\u0000 </mrow>\u0000 <annotation>$p,q$</annotation>\u0000 </semantics></math>. Moreover, our construction can be generalised from parabolas to a family of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$C^2$</annotation>\u0000 </semantics></math> curves satisfying suitable curvature conditions.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2531-2548"},"PeriodicalIF":0.9,"publicationDate":"2025-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Corrigendum: Graph bundles and Ricci-flatness 勘误:图束和里奇平坦度
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-29 DOI: 10.1112/blms.70111
Wenbo Li, Shiping Liu
{"title":"Corrigendum: Graph bundles and Ricci-flatness","authors":"Wenbo Li,&nbsp;Shiping Liu","doi":"10.1112/blms.70111","DOIUrl":"10.1112/blms.70111","url":null,"abstract":"<p>This note is a corrigendum to the authors' paper “Graph bundles and Ricci–flatness, Bulletin of the London Mathematical Society, 56(2), pp. 523–535, 2024”.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 6","pages":"1921-1922"},"PeriodicalIF":0.9,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70111","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144245168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Ohta–Kawasaki model set on the space 一个大田川崎模型设置在空间
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-29 DOI: 10.1112/blms.70105
Lorena Aguirre Salazar, Xin Yang Lu, Jun-cheng Wei
{"title":"An Ohta–Kawasaki model set on the space","authors":"Lorena Aguirre Salazar,&nbsp;Xin Yang Lu,&nbsp;Jun-cheng Wei","doi":"10.1112/blms.70105","DOIUrl":"10.1112/blms.70105","url":null,"abstract":"<p>We examine a nonlocal diffuse interface energy with Coulomb repulsion in three dimensions inspired by the Thomas–Fermi–Dirac–von Weizsäcker, and the Ohta–Kawasaki models. We consider the corresponding mass-constrained variational problem and show the existence of minimizers for small masses, and the absence of minimizers for large masses.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2462-2476"},"PeriodicalIF":0.9,"publicationDate":"2025-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815248","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Thurston obstructions and tropical geometry 瑟斯顿障碍物和热带几何
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-27 DOI: 10.1112/blms.70102
Rohini Ramadas
{"title":"Thurston obstructions and tropical geometry","authors":"Rohini Ramadas","doi":"10.1112/blms.70102","DOIUrl":"10.1112/blms.70102","url":null,"abstract":"<p>We describe an application of tropical moduli spaces to complex dynamics. A post-critically finite branched covering <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$S^2$</annotation>\u0000 </semantics></math> induces a pullback map on the Teichmüller space of complex structures of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$S^2$</annotation>\u0000 </semantics></math>; this descends to an algebraic correspondence on the moduli space of point-configurations of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>P</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$mathbb {P}^1$</annotation>\u0000 </semantics></math>. We make a case for studying the action of the tropical moduli space correspondence by making explicit the connections between objects that have come up in one guise in tropical geometry and in another guise in complex dynamics. For example, a Thurston obstruction for <span></span><math>\u0000 <semantics>\u0000 <mi>φ</mi>\u0000 <annotation>$varphi$</annotation>\u0000 </semantics></math> corresponds to a ray that is fixed by the tropical moduli space correspondence, and scaled by a factor <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$geqslant 1$</annotation>\u0000 </semantics></math>. This article is intended to be accessible to algebraic and tropical geometers as well as to complex dynamicists.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2404-2428"},"PeriodicalIF":0.9,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70102","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815157","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Multiplicities of weakly graded families of ideals 弱等级理想族的多样性
IF 0.9 3区 数学
Bulletin of the London Mathematical Society Pub Date : 2025-05-27 DOI: 10.1112/blms.70099
Parangama Sarkar
{"title":"Multiplicities of weakly graded families of ideals","authors":"Parangama Sarkar","doi":"10.1112/blms.70099","DOIUrl":"10.1112/blms.70099","url":null,"abstract":"&lt;p&gt;In this article, we extend the notion of multiplicity for weakly graded families of ideals which are bounded below linearly. In particular, we show that the limit &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;e&lt;/mi&gt;\u0000 &lt;mi&gt;W&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;munder&gt;\u0000 &lt;mi&gt;lim&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;∞&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/munder&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;!&lt;/mo&gt;\u0000 &lt;mfrac&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;ℓ&lt;/mi&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;/&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;/mfrac&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$ e_W(mathcal {I}):=lim limits _{nrightarrow infty }d!frac{ell _R(R/I_n)}{n^d}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; exists where &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$mathcal {I}=lbrace I_nrbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; is a bounded below linearly weakly graded family of ideals in a Noetherian local ring &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;m&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$(R,mathfrak {m})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of dimension &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;⩾&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$dgeqslant 1$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; with &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;dim&lt;/mo","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2354-2371"},"PeriodicalIF":0.9,"publicationDate":"2025-05-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815158","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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