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

{"title":"L\u0000 p\u0000 \u0000 $L^p$\u0000 -bounds in Safarov pseudo-differential calculus on manifolds with bounded geometry","authors":"Santiago Gómez Cobos, Michael Ruzhansky","doi":"10.1112/jlms.70145","DOIUrl":"https://doi.org/10.1112/jlms.70145","url":null,"abstract":"<p>Given a smooth complete Riemannian manifold with bounded geometry <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>,</mo>\u0000 <mi>g</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$(M,g)$</annotation>\u0000 </semantics></math> and a linear connection <span></span><math>\u0000 <semantics>\u0000 <mo>∇</mo>\u0000 <annotation>$nabla$</annotation>\u0000 </semantics></math> on it (not necessarily a metric one), we prove 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>-boundedness of operators belonging to the global pseudo-differential classes <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>Ψ</mi>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 <mo>,</mo>\u0000 <mi>δ</mi>\u0000 </mrow>\u0000 <mi>m</mi>\u0000 </msubsup>\u0000 <mfenced>\u0000 <msup>\u0000 <mi>Ω</mi>\u0000 <mi>κ</mi>\u0000 </msup>\u0000 <mo>,</mo>\u0000 <mo>∇</mo>\u0000 <mo>,</mo>\u0000 <mi>τ</mi>\u0000 </mfenced>\u0000 </mrow>\u0000 <annotation>$Psi _{rho, delta }^mleft(Omega ^kappa, nabla, tau right)$</annotation>\u0000 </semantics></math> constructed by Safarov. Our result recovers classical Fefferman's theorem, and extends it to the following two situations: <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>ρ</mi>\u0000 <mo>></mo>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$rho >1/3$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mo>∇</mo>\u0000 <annotation>$nabla$</annotation>\u0000 </semantics></math> symmetric; and <span></span><math>\u0000 <semantics>\u0000 <mo>∇</mo>\u0000 <annotation>$nabla$</annotation>\u0000 </semantics></math> flat with any values of <span></span><math>\u0000 <semantics>\u0000 <mi>ρ</mi>\u0000 <annotation>$rho$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mi>δ</mi>\u0000 <annotation>$delta$</annotation>\u0000 </semantics></math>. Moreover, as a consequence of our main result, we obtain boundedness on Sobolev and Besov spaces and some <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143831219","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":"The Alexander and Markov theorems for strongly involutive links","authors":"Alice Merz","doi":"10.1112/jlms.70156","DOIUrl":"https://doi.org/10.1112/jlms.70156","url":null,"abstract":"<p>The Alexander theorem (1923) and the Markov theorem (1936) are two classical results in knot theory that show, respectively, that every link is the closure of a braid and that braids that have the same closure are related by a finite number of operations called Markov moves. This paper presents specialised versions of these two classical theorems for a class of links in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mn>3</mn>\u0000 </msup>\u0000 <annotation>$S^3$</annotation>\u0000 </semantics></math> preserved by an involution, that we call strongly involutive links. When connected, these links are known as strongly invertible knots, and have been extensively studied. We develop an equivariant closure map that, given two palindromic braids, produces a strongly involutive link. We demonstrate that this map is surjective up to equivalence of strongly involutive links. Furthermore, we establish that pairs of palindromic braids that have the same equivariant closure are related by an equivariant version of the original Markov moves.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826810","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":"An example of \u0000 \u0000 \u0000 A\u0000 2\u0000 \u0000 $A_2$\u0000 Rogers–Ramanujan bipartition identities of level 3","authors":"Shunsuke Tsuchioka","doi":"10.1112/jlms.70152","DOIUrl":"https://doi.org/10.1112/jlms.70152","url":null,"abstract":"<p>We give manifestly positive Andrews–Gordon type series for the level 3 standard modules of the affine Lie algebra of type <span></span><math>\u0000 <semantics>\u0000 <msubsup>\u0000 <mi>A</mi>\u0000 <mn>2</mn>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msubsup>\u0000 <annotation>$A^{(1)}_2$</annotation>\u0000 </semantics></math>. We also give corresponding bipartition identities, which have representation theoretic interpretations via the vertex operators. Our proof is based on the Borodin product formula, the Corteel–Welsh recursion for the cylindric partitions, a <span></span><math>\u0000 <semantics>\u0000 <mi>q</mi>\u0000 <annotation>$q$</annotation>\u0000 </semantics></math>-version of Sister Celine's technique and a generalization of Andrews' partition ideals by finite automata due to Takigiku and the author.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826798","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":"The minima of the geodesic length functions of uniform filling curves","authors":"Ernesto Girondo,&nbsp;Gabino González-Diez,&nbsp;Rubén A. Hidalgo","doi":"10.1112/jlms.70153","DOIUrl":"https://doi.org/10.1112/jlms.70153","url":null,"abstract":"<p>There is a natural link between (multi-)curves that fill up a closed oriented surface and dessins d'enfants. We use this approach to exhibit explicitly the minima of the geodesic length function of filling curves that admit a self-transverse homotopy equivalent representative such that all self-intersection points, as well as all faces of the complement, have the same multiplicity. We show that these minima are attained at the Grothendieck–Belyi surfaces determined by the natural dessin d'enfants associated with these filling curves. In particular, they are all Riemann surfaces defined over number fields.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826799","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":"Density functions for epsilon multiplicity and families of ideals","authors":"Suprajo Das,&nbsp;Sudeshna Roy,&nbsp;Vijaylaxmi Trivedi","doi":"10.1112/jlms.70155","DOIUrl":"https://doi.org/10.1112/jlms.70155","url":null,"abstract":"&lt;p&gt;A density function for an algebraic invariant is a measurable function 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; which &lt;i&gt;measures&lt;/i&gt; the invariant on an &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;-scale. This function carries a lot more information related to the invariant without seeking extra data. It has turned out to be a useful tool, which was introduced by the third author in Trivedi [Trans. Amer. Math. Soc. &lt;b&gt;370&lt;/b&gt; (2018), no. 12, 8403–8428], to study the characteristic &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;annotation&gt;$p$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; invariant, namely Hilbert–Kunz multiplicity of a homogeneous &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;${bf m}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;-primary ideal. Here, we construct &lt;i&gt;density functions&lt;/i&gt; &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&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;/msub&gt;\u0000 &lt;annotation&gt;$f_{A,lbrace I_nrbrace }$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; for a Noetherian filtration &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;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;mi&gt;n&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;N&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;annotation&gt;$lbrace I_nrbrace _{nin {mathbb {N}}}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; of homogeneous ideals and &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;A&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;mover&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;I&lt;/mi&gt;\u0000 &lt;mi&gt;n&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;∼&lt;/mo&gt;\u0000 &lt;/mover&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mr","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70155","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143826811","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":"Quantitative results on symplectic barriers","authors":"Pazit Haim-Kislev,&nbsp;Richard Hind,&nbsp;Yaron Ostrover","doi":"10.1112/jlms.70144","DOIUrl":"https://doi.org/10.1112/jlms.70144","url":null,"abstract":"<p>In this paper, we present some quantitative results concerning symplectic barriers. In particular, we answer a question raised by Sackel, Song, Varolgunes, and Zhu regarding the symplectic size of the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$2n$</annotation>\u0000 </semantics></math>-dimensional Euclidean ball with a codimension-two linear subspace removed.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143822087","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":"Linear response for random and sequential intermittent maps","authors":"Davor Dragičević,&nbsp;Cecilia González-Tokman,&nbsp;Julien Sedro","doi":"10.1112/jlms.70150","DOIUrl":"https://doi.org/10.1112/jlms.70150","url":null,"abstract":"<p>This work establishes a quenched (trajectory-wise) linear response formula for random intermittent dynamical systems, consisting of Liverani–Saussol–Vaienti maps with varying parameters. This result complements recent annealed (averaged) results in the independent and identically distributed setting. As an intermediate step, we show existence, uniqueness and statistical stability of the random absolutely continuous invariant probability measure for such nonuniformly expanding systems. Furthermore, we investigate sequential intermittent dynamical systems of this type and establish a linear response formula. Our arguments rely on the cone technique introduced by Baladi and Todd and further developed by Leppänen. We also demonstrate that sequential systems exhibit a subtle distinction from both random and autonomous settings: they may possess infinitely many sequential absolutely continuous equivariant densities. However, only one of these corresponds to an SRB state in the sense of Ruelle.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70150","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818438","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":"Asymptotic normality of pattern occurrences in random maps","authors":"Michael Drmota,&nbsp;Eva-Maria Hainzl,&nbsp;Nick Wormald","doi":"10.1112/jlms.70149","DOIUrl":"https://doi.org/10.1112/jlms.70149","url":null,"abstract":"<p>The purpose of this paper is to study the limiting distribution of special <i>additive functionals</i> on random planar maps, namely the number of occurrences of a given <i>pattern</i>. The main result is a central limit theorem for these pattern counts in the case of patterns with a simple boundary. The proof relies on a combination of analytic and combinatorial methods together with a moment method due to Gao and Wormald [Probab. Theory Relat. Fields <b>130</b> (2004), 368–376]. It is an important issue to handle the overlap structure of two patterns which is the main difficulty in the proof.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818608","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":"Partial regularity for variational integrals with Morrey–Hölder zero-order terms, and the limit exponent in Massari's regularity theorem","authors":"Thomas Schmidt,&nbsp;Jule Helena Schütt","doi":"10.1112/jlms.70139","DOIUrl":"https://doi.org/10.1112/jlms.70139","url":null,"abstract":"<p>We revisit the partial <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>,</mo>\u0000 <mi>α</mi>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathrm{C}^{1,alpha }$</annotation>\u0000 </semantics></math> regularity theory for minimizers of non-parametric integrals with emphasis on sharp dependence of the Hölder exponent <span></span><math>\u0000 <semantics>\u0000 <mi>α</mi>\u0000 <annotation>$alpha$</annotation>\u0000 </semantics></math> on structural assumptions for general zero-order terms. A particular case of our conclusions carries over to the parametric setting of Massari's regularity theorem for prescribed-mean-curvature hypersurfaces and there confirms optimal regularity up to the limit exponent.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70139","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143818607","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":"Quantitative expansivity for ergodic \u0000 \u0000 \u0000 Z\u0000 d\u0000 \u0000 $mathbb {Z}^d$\u0000 -actions","authors":"Alexander Fish,&nbsp;Sean Skinner","doi":"10.1112/jlms.70154","DOIUrl":"https://doi.org/10.1112/jlms.70154","url":null,"abstract":"<p>We study expansiveness properties of positive measure subsets of ergodic <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {Z}^d$</annotation>\u0000 </semantics></math>-actions along two different types of structured subsets of <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>Z</mi>\u0000 <mi>d</mi>\u0000 </msup>\u0000 <annotation>$mathbb {Z}^d$</annotation>\u0000 </semantics></math>, namely, cyclic subgroups and images of integer polynomials. We prove quantitative expansiveness properties in both cases, strengthening combinatorial results from two distinct works—one by Björklund and Fish, the other by Bulinski and Fish. Our methods unify and strengthen earlier approaches used in Björklund and Fish and Bulinski and Fish and to our surprise, also yield a counterexample to a certain pinned variant of the polynomial Bogolyubov theorem.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 4","pages":""},"PeriodicalIF":1.0,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70154","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143809491","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}