Bulletin of the London Mathematical Society最新文献

{"title":"Corrigendum: Graph bundles and Ricci-flatness","authors":"Wenbo Li,&nbsp;Shiping Liu","doi":"10.1112/blms.70111","DOIUrl":"https://doi.org/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":0.8,"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}

{"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":"https://doi.org/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}

{"title":"Thurston obstructions and tropical geometry","authors":"Rohini Ramadas","doi":"10.1112/blms.70102","DOIUrl":"https://doi.org/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}

{"title":"Asymptotic Behavior of the Bergman Metric at Infinite Type Points","authors":"Ravi Shankar Jaiswal","doi":"10.1112/blms.70100","DOIUrl":"https://doi.org/10.1112/blms.70100","url":null,"abstract":"<p>We investigate nontangential asymptotic limits of the Bergman kernel on the diagonal, and the Bergman metric and its holomorphic sectional curvature at exponentially flat infinite-type boundary points of smooth bounded pseudoconvex domains in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>+</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$mathbb {C}^{n + 1}$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>∈</mo>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$n in mathbb {N}$</annotation>\u0000 </semantics></math>. After showing that these objects satisfy the appropriate localizations, we apply the method of scaling to prove our results.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2372-2394"},"PeriodicalIF":0.9,"publicationDate":"2025-05-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815214","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}

{"title":"Eigenvalue estimate for the \u0000 \u0000 p\u0000 $p$\u0000 -Laplace operator on a connected finite graph","authors":"Lin Feng Wang","doi":"10.1112/blms.70104","DOIUrl":"https://doi.org/10.1112/blms.70104","url":null,"abstract":"<p>In this paper, we consider eigenvalue estimate for the <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>-Laplace operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$triangle _p$</annotation>\u0000 </semantics></math> on a connected finite graph with the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>CD</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathrm{CD}_p(m,0)$</annotation>\u0000 </semantics></math> condition for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>p</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$p&gt;1$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>m</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>0</mn>\u0000 </mrow>\u0000 <annotation>$m&gt;0$</annotation>\u0000 </semantics></math>. We first establish elliptic gradient estimates for solutions to the eigenvalue equation. Then we establish a lower bound estimate for the first nonzero eigenvalue of <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>p</mi>\u0000 </msub>\u0000 <annotation>$triangle _p$</annotation>\u0000 </semantics></math>, which is a generalization not only of the eigenvalue estimate for the manifold setting, but also of the eigenvalue estimate for the <span></span><math>\u0000 <semantics>\u0000 <mi>μ</mi>\u0000 <annotation>$mu$</annotation>\u0000 </semantics></math>-Laplace operator <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>▵</mi>\u0000 <mi>μ</mi>\u0000 </msub>\u0000 <annotation>$triangle _{mu }$</annotation>\u0000 </semantics></math> on the graph with the <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>CD</mi>\u0000 <mo>(</mo>\u0000 <mi>m</mi>\u0000 <mo>,</mo>\u0000 <mn>0</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$mathrm{CD}(m,0)$</annotation>\u0000 </semantics></math> condition.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2444-2461"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815241","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}

{"title":"On Natário's Minkowski-type inequality in the hyperbolic space","authors":"Yong Wei","doi":"10.1112/blms.70106","DOIUrl":"https://doi.org/10.1112/blms.70106","url":null,"abstract":"<p>We apply Brendle–Guan–Li's inverse curvature–type flow to prove a family of sharp inequalities for curvature integrals and their rigidity results for hypersurfaces in the hyperbolic space. In particular, we provide a new short proof of Natário's Minkowski-type inequality and its rigidity for convex surfaces in the hyperbolic 3-space.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2477-2488"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815240","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}

{"title":"On Artin's conjecture on average and short character sums","authors":"Oleksiy Klurman,&nbsp;Igor E. Shparlinski,&nbsp;Joni Teräväinen","doi":"10.1112/blms.70103","DOIUrl":"https://doi.org/10.1112/blms.70103","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>a</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_a(x)$</annotation>\u0000 </semantics></math> denote the number of primes up to <span></span><math>\u0000 <semantics>\u0000 <mi>x</mi>\u0000 <annotation>$x$</annotation>\u0000 </semantics></math> for which the integer <span></span><math>\u0000 <semantics>\u0000 <mi>a</mi>\u0000 <annotation>$a$</annotation>\u0000 </semantics></math> is a primitive root. We show that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>N</mi>\u0000 <mi>a</mi>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$N_a(x)$</annotation>\u0000 </semantics></math> satisfies the asymptotic predicted by Artin's conjecture for almost all <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>a</mi>\u0000 <mo>⩽</mo>\u0000 <mi>exp</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>log</mi>\u0000 <mi>log</mi>\u0000 <mi>x</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$1leqslant aleqslant exp ((log log x)^2)$</annotation>\u0000 </semantics></math>. This improves on a result of Stephens (1969). A key ingredient in the proof is a new short character sum estimate over the integers, improving on the range of a result of Garaev (2006).</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2429-2443"},"PeriodicalIF":0.9,"publicationDate":"2025-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://londmathsoc.onlinelibrary.wiley.com/doi/epdf/10.1112/blms.70103","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815242","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}

{"title":"A note on combinatorial invariance of Kazhdan–Lusztig polynomials","authors":"Francesco Esposito,&nbsp;Mario Marietti","doi":"10.1112/blms.70101","DOIUrl":"https://doi.org/10.1112/blms.70101","url":null,"abstract":"<p>We introduce the concepts of an amazing hypercube decomposition and a double shortcut for it, and use these new ideas to formulate a conjecture implying the combinatorial invariance conjecture for the Kazhdan–Lusztig polynomials of the symmetric group. This conjecture has the advantage of being combinatorial in nature. The appendix by Barkley and Gaetz discusses the related notion of double hypercubes and proves an analogous conjecture for these in the case of co-elementary intervals.</p>","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2395-2403"},"PeriodicalIF":0.9,"publicationDate":"2025-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815137","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}

{"title":"Dimension-free Fourier restriction inequalities","authors":"Diogo Oliveira e Silva,&nbsp;Błażej Wróbel","doi":"10.1112/blms.70098","DOIUrl":"https://doi.org/10.1112/blms.70098","url":null,"abstract":"&lt;p&gt;Let &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;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&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;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;${{bf R}_{mathbb {S}^{d-1}}}(prightarrow q)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; denote the best constant for the &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;L&lt;/mi&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&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;/msup&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$L^p(mathbb {R}^d)rightarrow L^q(mathbb {S}^{d-1})$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; Fourier restriction inequality to the unit sphere &lt;span&gt;&lt;/span&gt;&lt;math&gt;\u0000 &lt;semantics&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&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;/msup&gt;\u0000 &lt;annotation&gt;$mathbb {S}^{d-1}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;, and let &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;R&lt;/mi&gt;\u0000 &lt;msup&gt;\u0000 &lt;mi&gt;S&lt;/mi&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;/msup&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;q&lt;/mi&gt;\u0000 &lt;mo&gt;;&lt;/mo&gt;\u0000 &lt;mi&gt;r&lt;/mi&gt;\u0000 &lt;mi&gt;a&lt;/mi&gt;\u0000 ","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2336-2353"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144815151","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}

{"title":"Heisenberg uniqueness pairs and the wave equation","authors":"Shanlin Huang,&nbsp;Jiaqi Yu","doi":"10.1112/blms.70095","DOIUrl":"https://doi.org/10.1112/blms.70095","url":null,"abstract":"&lt;p&gt;The concept of the Heisenberg uniqueness pair &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;Γ&lt;/mi&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;/mrow&gt;\u0000 &lt;annotation&gt;$(Gamma, Lambda)$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; was introduced by Hedenmalm and Montes-Rodríguez as a variant of the uncertainty principle for the Fourier transform. The main results in Hedenmalm and Montes-Rodríguez (Ann. of Math. (2) &lt;b&gt;173&lt;/b&gt; (2011), 1507–1527) concern the hyperbola &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;Γ&lt;/mi&gt;\u0000 &lt;mi&gt;ε&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;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&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;msup&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mspace&gt;&lt;/mspace&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/msub&gt;\u0000 &lt;msub&gt;\u0000 &lt;mi&gt;x&lt;/mi&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/msub&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;/mrow&gt;\u0000 &lt;annotation&gt;$Gamma _{epsilon }=lbrace (x_1, x_2)in mathbb {R}^2,, x_1x_2=epsilon rbrace$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt; (&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;ε&lt;/mi&gt;\u0000 &lt;mo&gt;∈&lt;/mo&gt;\u0000 &lt;mi&gt;R&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;annotation&gt;$0ne epsilon in mathbb {R}$&lt;/annotation&gt;\u0000 &lt;/semantics&gt;&lt;/math&gt;) and lattice-crosses &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;Λ&lt;/mi&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;α&lt;/mi&gt;\u0000 &lt;mi&gt;β&lt;/mi&gt;\u0000 &lt;/mrow&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;α&lt;/mi&gt;\u0000 &lt;mi&gt;Z&lt;/mi&gt;\u0000 &lt;mo&gt;×&lt;/mo&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;","PeriodicalId":55298,"journal":{"name":"Bulletin of the London Mathematical Society","volume":"57 8","pages":"2286-2310"},"PeriodicalIF":0.9,"publicationDate":"2025-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814589","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}