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

{"title":"On curvature bounds in Lorentzian length spaces","authors":"Tobias Beran,&nbsp;Michael Kunzinger,&nbsp;Felix Rott","doi":"10.1112/jlms.12971","DOIUrl":"https://doi.org/10.1112/jlms.12971","url":null,"abstract":"<p>We introduce several new notions of (sectional) curvature bounds for Lorentzian pre-length spaces: On the one hand, we provide convexity/concavity conditions for the (modified) time separation function, and, on the other hand, we study four-point conditions, which are suitable also for the non-intrinsic setting. Via these concepts, we are able to establish (under mild assumptions) the equivalence of all previously known formulations of curvature bounds. In particular, we obtain the equivalence of causal and timelike curvature bounds as introduced by Kunzinger and Sämann.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12971","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968335","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":"Blowup algebras of determinantal ideals in prime characteristic","authors":"Alessandro De Stefani,&nbsp;Jonathan Montaño,&nbsp;Luis Núñez-Betancourt","doi":"10.1112/jlms.12969","DOIUrl":"https://doi.org/10.1112/jlms.12969","url":null,"abstract":"<p>We study when blowup algebras are <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-split or strongly <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-regular. Our main focus is on algebras given by symbolic and ordinary powers of ideals of minors of a generic matrix, a symmetric matrix, and a Hankel matrix. We also study ideals of Pfaffians of a skew-symmetric matrix. We use these results to obtain bounds on the degrees of the defining equations for these algebras. We also prove that the limit of the normalized regularity of the symbolic powers of these ideals exists and that their depth stabilizes. Finally, we show that, for determinantal ideals, there exists a monomial order for which taking initial ideals commutes with taking symbolic powers. To obtain these results, we develop the notion of <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-split filtrations and symbolic <span></span><math>\u0000 <semantics>\u0000 <mi>F</mi>\u0000 <annotation>$F$</annotation>\u0000 </semantics></math>-split ideals.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141967507","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":"New examples of 2-nondegenerate real hypersurfaces in \u0000 \u0000 \u0000 C\u0000 N\u0000 \u0000 $mathbb {C}^N$\u0000 with arbitrary nilpotent symbols","authors":"Martin Kolář,&nbsp;Ilya Kossovskiy,&nbsp;David Sykes","doi":"10.1112/jlms.12962","DOIUrl":"https://doi.org/10.1112/jlms.12962","url":null,"abstract":"<p>We introduce a class of uniformly 2-nondegenerate CR hypersurfaces in <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>C</mi>\u0000 <mi>N</mi>\u0000 </msup>\u0000 <annotation>$mathbb {C}^N$</annotation>\u0000 </semantics></math>, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$N&amp;gt;3$</annotation>\u0000 </semantics></math>, having a rank 1 Levi kernel. The class is first of all remarkable by the fact that for every <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>3</mn>\u0000 </mrow>\u0000 <annotation>$N&amp;gt;3$</annotation>\u0000 </semantics></math> it forms an <i>explicit</i> infinite-dimensional family of everywhere 2-nondegenerate hypersurfaces. To the best of our knowledge, this is the first such construction. Besides, the class contains infinite-dimensional families of nonequivalent structures having a given constant nilpotent CR symbol for every such symbol. Using methods that are able to handle all cases with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>5</mn>\u0000 </mrow>\u0000 <annotation>$N&amp;gt;5$</annotation>\u0000 </semantics></math> simultaneously, we solve the equivalence problem for the considered structures whose symbol is represented by a single Jordan block, classify their algebras of infinitesimal symmetries, and classify the locally homogeneous structures among them. We show that the remaining considered structures, which have symbols represented by a direct sum of Jordan blocks, can be constructed from the single block structures through simple linking and extension processes.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736850","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":"Sublinear bilipschitz equivalence and sublinearly Morse boundaries","authors":"Gabriel Pallier,&nbsp;Yulan Qing","doi":"10.1112/jlms.12960","DOIUrl":"https://doi.org/10.1112/jlms.12960","url":null,"abstract":"<p>A sublinear bilipschitz equivalence (SBE) between metric spaces is a map from one space to another that distorts distances with bounded multiplicative constants and sublinear additive error. Given any sublinear function, the associated sublinearly Morse boundaries are defined for all geodesic proper metric spaces as a quasi-isometrically invariant and metrizable topological space of quasi-geodesic rays. In this paper, we prove that sublinearly-Morse boundaries of proper geodesic metric spaces are invariant under suitable SBEs. A tool in the proof is the use of sublinear rays, that is, sublinear bilispchitz embeddings of the half line, generalizing quasi-geodesic rays. As an application, we distinguish a pair of right-angled Coxeter groups brought up by Behrstock up to SBE. We also show that under mild assumptions, generic random walks on countable groups are sublinear rays.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736849","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":"Estimates of the Kobayashi metric and Gromov hyperbolicity on convex domains of finite type","authors":"Hongyu Wang","doi":"10.1112/jlms.12966","DOIUrl":"https://doi.org/10.1112/jlms.12966","url":null,"abstract":"<p>In this paper, we give a local estimate for the Kobayashi distance on a bounded convex domain of finite type, which relates to a local pseudodistance near the boundary. The estimate is precise up to a bounded additive term. Also, we conclude that the domain equipped with the Kobayashi distance is Gromov hyperbolic that gives another proof of the result of Zimmer.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141736848","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":"Applying projective functors to arbitrary holonomic simple modules","authors":"Marco Mackaay,&nbsp;Volodymyr Mazorchuk,&nbsp;Vanessa Miemietz","doi":"10.1112/jlms.12965","DOIUrl":"https://doi.org/10.1112/jlms.12965","url":null,"abstract":"<p>We prove that applying a projective functor to a holonomic simple module over a semisimple finite-dimensional complex Lie algebra produces a module that has an essential semisimple submodule of finite length. This implies that holonomic simple supermodules over certain Lie superalgebras are quotients of modules that are induced from simple modules over the even part. We also provide some further insight into the structure of Lie algebra modules that are obtained by applying projective functors to simple modules.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12965","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639500","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":"P. Jones' interpolation theorem for noncommutative martingale Hardy spaces II","authors":"Narcisse Randrianantoanina","doi":"10.1112/jlms.12968","DOIUrl":"https://doi.org/10.1112/jlms.12968","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math> be a semifinite von Neumann algebra equipped with an increasing filtration <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$(mathcal {M}_n)_{ngeqslant 1}$</annotation>\u0000 </semantics></math> of (semifinite) von Neumann subalgebras of <span></span><math>\u0000 <semantics>\u0000 <mi>M</mi>\u0000 <annotation>$mathcal {M}$</annotation>\u0000 </semantics></math>. For <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>⩽</mo>\u0000 <mi>p</mi>\u0000 <mo>⩽</mo>\u0000 <mi>∞</mi>\u0000 </mrow>\u0000 <annotation>$1leqslant p leqslant infty$</annotation>\u0000 </semantics></math>, let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msubsup>\u0000 <mi>H</mi>\u0000 <mi>p</mi>\u0000 <mi>c</mi>\u0000 </msubsup>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>M</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$mathcal {H}_p^c(mathcal {M})$</annotation>\u0000 </semantics></math> denote the noncommutative column martingale Hardy space constructed from column square functions associated with the filtration <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <msub>\u0000 <mi>M</mi>\u0000 <mi>n</mi>\u0000 </msub>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>⩾</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msub>\u0000 <annotation>$(mathcal {M}_n)_{ngeqslant 1}$</annotation>\u0000 </semantics></math> and the index <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. We prove the following real interpolation identity: If <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>0</mn>\u0000 <mo>&lt;</mo>\u0000 <mi>θ</mi>\u0000 <mo>&lt;</mo>\u0000 <mn>1</mn>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141639563","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":"Subrank and optimal reduction of scalar multiplications to generic tensors","authors":"Harm Derksen,&nbsp;Visu Makam,&nbsp;Jeroen Zuiddam","doi":"10.1112/jlms.12963","DOIUrl":"https://doi.org/10.1112/jlms.12963","url":null,"abstract":"<p>The subrank of a tensor measures how much a tensor can be diagonalized. We determine this parameter precisely for essentially all (i.e., generic) tensors. Namely, we prove for generic tensors in <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>V</mi>\u0000 <mo>⊗</mo>\u0000 <mi>V</mi>\u0000 <mo>⊗</mo>\u0000 <mi>V</mi>\u0000 </mrow>\u0000 <annotation>$V otimes V otimes V$</annotation>\u0000 </semantics></math> with <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mo>dim</mo>\u0000 <mo>(</mo>\u0000 <mi>V</mi>\u0000 <mo>)</mo>\u0000 <mo>=</mo>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 <annotation>$dim (V) = n$</annotation>\u0000 </semantics></math> that the subrank is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Θ</mi>\u0000 <mo>(</mo>\u0000 <msqrt>\u0000 <mi>n</mi>\u0000 </msqrt>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Theta (sqrt {n})$</annotation>\u0000 </semantics></math>. Our result significantly improves on the previous upper bound from the work of Strassen (1991) and Bürgisser (1990) which was <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>2</mn>\u0000 <mo>/</mo>\u0000 <mn>3</mn>\u0000 <mo>+</mo>\u0000 <mi>o</mi>\u0000 <mo>(</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <annotation>$n^{2/3+o(1)}$</annotation>\u0000 </semantics></math>. Our result is tight up to an additive constant. Our full result covers not only 3-tensors but also <span></span><math>\u0000 <semantics>\u0000 <mi>k</mi>\u0000 <annotation>$k$</annotation>\u0000 </semantics></math>-tensors, for which we find that the generic subrank is <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>Θ</mi>\u0000 <mo>(</mo>\u0000 <msup>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 <mo>/</mo>\u0000 <mo>(</mo>\u0000 <mi>k</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </msup>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$Thet","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12963","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141608101","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":"Intersection matrices for the minimal regular model of \u0000 \u0000 \u0000 \u0000 X\u0000 0\u0000 \u0000 \u0000 (\u0000 N\u0000 )\u0000 \u0000 \u0000 ${X}_0(N)$\u0000 and applications to the Arakelov canonical sheaf","authors":"Paolo Dolce,&nbsp;Pietro Mercuri","doi":"10.1112/jlms.12964","DOIUrl":"https://doi.org/10.1112/jlms.12964","url":null,"abstract":"<p>Let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>&gt;</mo>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 <annotation>$N&amp;gt;1$</annotation>\u0000 </semantics></math> be an integer coprime to 6 such that <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>N</mi>\u0000 <mo>∉</mo>\u0000 <mo>{</mo>\u0000 <mn>5</mn>\u0000 <mo>,</mo>\u0000 <mn>7</mn>\u0000 <mo>,</mo>\u0000 <mn>13</mn>\u0000 <mo>}</mo>\u0000 </mrow>\u0000 <annotation>$Nnotin lbrace 5,7,13rbrace$</annotation>\u0000 </semantics></math> and let <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>g</mi>\u0000 <mo>=</mo>\u0000 <mi>g</mi>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$g=g(N)$</annotation>\u0000 </semantics></math> be the genus of the modular curve <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math>. We compute the intersection matrices relative to special fibres of the minimal regular model of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math>. Moreover, we prove that the self-intersection of the Arakelov canonical sheaf of <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>X</mi>\u0000 <mn>0</mn>\u0000 </msub>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>N</mi>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$X_0(N)$</annotation>\u0000 </semantics></math> is asymptotic to <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mn>3</mn>\u0000 <mi>g</mi>\u0000 <mi>log</mi>\u0000 <mi>N</mi>\u0000 </mrow>\u0000 <annotation>$3glog N$</annotation>\u0000 </semantics></math>, for <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 ","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597079","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":"Spectral constant rigidity of warped product metrics","authors":"Xiaoxiang Chai,&nbsp;Juncheol Pyo,&nbsp;Xueyuan Wan","doi":"10.1112/jlms.12958","DOIUrl":"https://doi.org/10.1112/jlms.12958","url":null,"abstract":"<p>A theorem of Llarull says that if a smooth metric <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> on the <span></span><math>\u0000 <semantics>\u0000 <mi>n</mi>\u0000 <annotation>$n$</annotation>\u0000 </semantics></math>-sphere <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>S</mi>\u0000 <mi>n</mi>\u0000 </msup>\u0000 <annotation>$mathbb {S}^n$</annotation>\u0000 </semantics></math> is bounded below by the standard round metric and the scalar curvature <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$R_g$</annotation>\u0000 </semantics></math> of <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> is bounded below by <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 <annotation>$n (n - 1)$</annotation>\u0000 </semantics></math>, then the metric <span></span><math>\u0000 <semantics>\u0000 <mi>g</mi>\u0000 <annotation>$g$</annotation>\u0000 </semantics></math> must be the standard round metric. We prove a spectral Llarull theorem by replacing the bound <span></span><math>\u0000 <semantics>\u0000 <mrow>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <mo>⩾</mo>\u0000 <mi>n</mi>\u0000 <mrow>\u0000 <mo>(</mo>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>1</mn>\u0000 <mo>)</mo>\u0000 </mrow>\u0000 </mrow>\u0000 <annotation>$R_g geqslant n (n - 1)$</annotation>\u0000 </semantics></math> by a lower bound on the first eigenvalue of an elliptic operator involving the Laplacian and the scalar curvature <span></span><math>\u0000 <semantics>\u0000 <msub>\u0000 <mi>R</mi>\u0000 <mi>g</mi>\u0000 </msub>\u0000 <annotation>$R_g$</annotation>\u0000 </semantics></math>. We utilize two methods: spinor and spacetime harmonic function.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2024-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12958","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141488322","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}