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Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle. 各向异性r<s:1>熵和海森堡测不准原理的锐上界。
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2026-01-01 Epub Date: 2026-03-14 DOI: 10.1007/s00229-026-01694-7
Marianna Chatzakou, Michael Ruzhansky, Anjali Shriwastawa
{"title":"Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle.","authors":"Marianna Chatzakou, Michael Ruzhansky, Anjali Shriwastawa","doi":"10.1007/s00229-026-01694-7","DOIUrl":"10.1007/s00229-026-01694-7","url":null,"abstract":"<p><p>In this paper, we prove the anisotropic Shannon inequality for the Rényi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a logarithmic Sobolev inequality in the setting of stratified groups, we prove a Heisenberg-type uncertainty principle in the latter setting.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"177 2","pages":"24"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12988971/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147469840","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Schubert cells and Whittaker functionals for GL ( r , R ) part I: Combinatorics. GL （r, r）的Schubert单元和Whittaker泛函第一部分：组合学。
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2026-01-01 Epub Date: 2026-06-05 DOI: 10.1007/s00229-026-01726-2
Doyon Kim
{"title":"<ArticleTitle xmlns:ns0=\"http://www.w3.org/1998/Math/MathML\">Schubert cells and Whittaker functionals for <ns0:math><ns0:mrow><ns0:mo>GL</ns0:mo> <ns0:mo>(</ns0:mo> <ns0:mi>r</ns0:mi> <ns0:mo>,</ns0:mo> <ns0:mi>R</ns0:mi> <ns0:mo>)</ns0:mo></ns0:mrow> </ns0:math> part I: Combinatorics.","authors":"Doyon Kim","doi":"10.1007/s00229-026-01726-2","DOIUrl":"https://doi.org/10.1007/s00229-026-01726-2","url":null,"abstract":"<p><p>We give a formula for a birational map on the Schubert cell associated to each Weyl group element of <math><mrow><mi>G</mi> <mo>=</mo> <mo>GL</mo> <mo>(</mo> <mi>r</mi> <mo>)</mo></mrow> </math> . The map simplifies the UDL decomposition of matrices, providing structural insight into the Schubert cell decomposition of the flag variety <i>G</i>/<i>B</i>, where <i>B</i> is a Borel subgroup. An application of the formula includes a new proof of the existence of Whittaker functionals for principal series representations of <math><mrow><mo>GL</mo> <mo>(</mo> <mi>r</mi> <mo>,</mo> <mi>R</mi> <mo>)</mo></mrow> </math> via integration by parts. In this paper, we establish combinatorial properties of the birational map and prove auxiliary results.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"177 3","pages":"40"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13241458/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148200888","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Topological groupoids with involution and real algebraic stacks. 具有对合和实代数堆栈的拓扑群。
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2026-01-01 Epub Date: 2026-06-26 DOI: 10.1007/s00229-026-01729-z
Emiliano Ambrosi, Olivier de Gaay Fortman
{"title":"Topological groupoids with involution and real algebraic stacks.","authors":"Emiliano Ambrosi, Olivier de Gaay Fortman","doi":"10.1007/s00229-026-01729-z","DOIUrl":"https://doi.org/10.1007/s00229-026-01729-z","url":null,"abstract":"<p><p>To a topological groupoid endowed with an involution, we associate a topological groupoid of fixed points, generalizing the fixed-point subspace of a topological space with involution. We prove that when the topological groupoid with involution arises from a Deligne-Mumford stack over <math><mi>R</mi></math> , this fixed locus coincides with the real locus of the stack. This provides a topological framework to study real algebraic stacks, and in particular real moduli spaces. Finally, we propose a Smith-Thom type conjecture in this setting, generalizing the Smith-Thom inequality for topological spaces endowed with an involution.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"177 4","pages":"47"},"PeriodicalIF":0.6,"publicationDate":"2026-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC13309455/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148347182","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Generalised killing spinors on three-dimensional Lie groups. 三维李群上的广义杀伤旋量。
IF 0.5 4区 数学
Manuscripta Mathematica Pub Date : 2025-01-01 Epub Date: 2025-02-07 DOI: 10.1007/s00229-025-01617-y
Diego Artacho
{"title":"Generalised killing spinors on three-dimensional Lie groups.","authors":"Diego Artacho","doi":"10.1007/s00229-025-01617-y","DOIUrl":"https://doi.org/10.1007/s00229-025-01617-y","url":null,"abstract":"<p><p>We present a complete classification of invariant generalised Killing spinors on three-dimensional Lie groups. We show that, in this context, the existence of a non-trivial invariant generalised Killing spinor implies that all invariant spinors are generalised Killing with the same endomorphism. Notably, this classification is independent of the choice of left-invariant metric. To illustrate the computational methods underlying this classification, we also provide the first known examples of homogeneous manifolds admitting invariant generalised Killing spinors with <i>n</i> distinct eigenvalues for each <math><mrow><mi>n</mi> <mo>></mo> <mn>4</mn></mrow> </math> .</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"176 1","pages":"15"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11861137/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143525096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Theta functions, broken lines and 2-marked log Gromov-Witten invariants. 函数，折线和2标记的log Gromov-Witten不变量。
IF 0.5 4区 数学
Manuscripta Mathematica Pub Date : 2025-01-01 Epub Date: 2025-06-19 DOI: 10.1007/s00229-025-01640-z
Tim Gräfnitz
{"title":"Theta functions, broken lines and 2-marked log Gromov-Witten invariants.","authors":"Tim Gräfnitz","doi":"10.1007/s00229-025-01640-z","DOIUrl":"10.1007/s00229-025-01640-z","url":null,"abstract":"<p><p>Theta functions were defined for varieties with effective anticanonical divisor [11] and are related to certain punctured Gromov-Witten invariants [2]. We show that in the case of a log Calabi-Yau surface (<i>X</i>, <i>D</i>) with smooth very ample anticanonical divisor we can relate theta functions and their multiplicative structure to certain 2-marked log Gromov-Witten invariants. This is a natural extension of the correspondence between wall functions and 1-marked log Gromov-Witten invariants [8]. It gives an enumerative interpretation for the intrinsic mirror construction of [17] and will be related to the open mirror map of outer Aganagic-Vafa branes in [9].</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"176 4","pages":"41"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12179237/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144477627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics. 非光滑黎曼和半黎曼度量的Ricci曲率界和刚性。
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2025-01-01 Epub Date: 2025-07-22 DOI: 10.1007/s00229-025-01655-6
Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso
{"title":"Ricci curvature bounds and rigidity for non-smooth Riemannian and semi-Riemannian metrics.","authors":"Michael Kunzinger, Argam Ohanyan, Alessio Vardabasso","doi":"10.1007/s00229-025-01655-6","DOIUrl":"10.1007/s00229-025-01655-6","url":null,"abstract":"<p><p>We study rigidity problems for Riemannian and semi-Riemannian manifolds with metrics of low regularity. Specifically, we prove a version of the Cheeger-Gromoll splitting theorem [22] for Riemannian metrics and the flatness criterion for semi-Riemannian metrics of regularity <math><msup><mi>C</mi> <mn>1</mn></msup> </math> . With our proof of the splitting theorem, we are able to obtain an isometry of higher regularity than the Lipschitz regularity guaranteed by the <math><mi>RCD</mi></math> -splitting theorem [30, 31]. Along the way, we establish a Bochner-Weitzenböck identity which permits both the non-smoothness of the metric and of the vector fields, complementing a recent similar result in [62]. The last section of the article is dedicated to the discussion of various notions of Sobolev spaces in low regularity, as well as an alternative proof of the equivalence (see [62]) between distributional Ricci curvature bounds and <math><mi>RCD</mi></math> -type bounds, using in part the stability of the variable <math><mi>CD</mi></math> -condition under suitable limits [47].</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"176 4","pages":"53"},"PeriodicalIF":0.6,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC12283871/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144709701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Quadratic Euler characteristic of symmetric powers of curves. 曲线对称幂的二次欧拉特性。
IF 0.5 4区 数学
Manuscripta Mathematica Pub Date : 2025-01-01 Epub Date: 2025-03-20 DOI: 10.1007/s00229-025-01623-0
Lukas F Bröring, Anna M Viergever
{"title":"Quadratic Euler characteristic of symmetric powers of curves.","authors":"Lukas F Bröring, Anna M Viergever","doi":"10.1007/s00229-025-01623-0","DOIUrl":"https://doi.org/10.1007/s00229-025-01623-0","url":null,"abstract":"<p><p>We compute the quadratic Euler characteristic of the symmetric powers of a smooth, projective curve over any field <i>k</i> that is not of characteristic two, using the Motivic Gauss-Bonnet Theorem of Levine-Raksit. As an application, we show that the power structure on the Grothendieck-Witt ring introduced by Pajwani-Pál computes the compactly supported <math> <msup><mrow><mi>A</mi></mrow> <mn>1</mn></msup> </math> -Euler characteristic of symmetric powers for all curves.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"176 2","pages":"26"},"PeriodicalIF":0.5,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC11926038/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143694132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Fano varieties of middle pseudoindex 中伪指数法诺变种
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-09-16 DOI: 10.1007/s00229-024-01593-9
Kiwamu Watanabe
{"title":"Fano varieties of middle pseudoindex","authors":"Kiwamu Watanabe","doi":"10.1007/s00229-024-01593-9","DOIUrl":"https://doi.org/10.1007/s00229-024-01593-9","url":null,"abstract":"<p>Let <i>X</i> be a complex smooth Fano variety of dimension <i>n</i>. In this paper, we give a classification of such <i>X</i> when the pseudoindex is equal to <span>(dfrac{dim X+1}{2})</span> and the Picard number greater than one.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"37 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142255329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 the reduced unramified Witt group of the product of two conics 论两个圆锥的乘积的还原无ramified 维特群
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-09-12 DOI: 10.1007/s00229-024-01591-x
Alexander S. Sivatski
{"title":"On the reduced unramified Witt group of the product of two conics","authors":"Alexander S. Sivatski","doi":"10.1007/s00229-024-01591-x","DOIUrl":"https://doi.org/10.1007/s00229-024-01591-x","url":null,"abstract":"<p>We investigate the reduced unramified Witt group of the product of two smooth projective conics <span>(X_1)</span>, <span>(X_2)</span> over a field. In some particular cases, this group denoted as <span>(W(X_1,X_2))</span> turns out to be very small (zero or <span>({mathbb {Z}}/2{mathbb {Z}})</span>). On the other hand, certain examples when it is infinite are constructed. We give sufficient conditions providing nontriviality of <span>(W(X_1,X_2))</span> in terms of 2-fold Pfister forms <span>(pi _1)</span>, <span>(pi _2)</span> associated with the conics. These conditions and constructions of the corresponding nonzero elements in <span>(W(X_1,X_2))</span> depend on <span>({text {ind}}(pi _1+pi _2))</span>. Also we study the question of triviality (nontriviality) of this group with respect to extensions of the ground field.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"60 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Deformation of Kähler metrics and an eigenvalue problem for the Laplacian on a compact Kähler manifold 凯勒流形的变形和紧凑凯勒流形上的拉普拉奇特征值问题
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-09-09 DOI: 10.1007/s00229-024-01592-w
Kazumasa Narita
{"title":"Deformation of Kähler metrics and an eigenvalue problem for the Laplacian on a compact Kähler manifold","authors":"Kazumasa Narita","doi":"10.1007/s00229-024-01592-w","DOIUrl":"https://doi.org/10.1007/s00229-024-01592-w","url":null,"abstract":"<p>We study an eigenvalue problem for the Laplacian on a compact Kähler manifold. Considering the <i>k</i>-th eigenvalue <span>(lambda _{k})</span> as a functional on the space of Kähler metrics with fixed volume on a compact complex manifold, we introduce the notion of <span>(lambda _{k})</span>-extremal Kähler metric. We deduce a condition for a Kähler metric to be <span>(lambda _{k})</span>-extremal. As examples, we consider product Kähler manifolds, compact isotropy irreducible homogeneous Kähler manifolds and flat complex tori.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"111 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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