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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":"https://doi.org/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
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
Log canonical pairs with conjecturally minimal volume 具有猜想最小体积的逻辑规范对
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-08-19 DOI: 10.1007/s00229-024-01588-6
Louis Esser, Burt Totaro
{"title":"Log canonical pairs with conjecturally minimal volume","authors":"Louis Esser, Burt Totaro","doi":"10.1007/s00229-024-01588-6","DOIUrl":"https://doi.org/10.1007/s00229-024-01588-6","url":null,"abstract":"<p>We construct log canonical pairs (<i>X</i>, <i>B</i>) with <i>B</i> a nonzero reduced divisor and <span>(K_X+B)</span> ample that have the smallest known volume. We conjecture that our examples have the smallest volume in each dimension. The conjecture is true in dimension 2, by Liu and Shokurov. The examples are weighted projective hypersurfaces that are not quasi-smooth. We also develop an example for a related extremal problem. Esser constructed a klt Calabi–Yau variety which conjecturally has the smallest mld in each dimension (for example, mld 1/13 in dimension 2 and 1/311 in dimension 3). However, the example was only worked out completely in dimensions at most 18. We now prove the desired properties of Esser’s example in all dimensions (in particular, determining its mld).</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"44 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142220394","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
Regulator of the Hesse cubic curves and hypergeometric functions 黑塞三次曲线和超几何函数的调节器
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-07-29 DOI: 10.1007/s00229-024-01587-7
Yusuke Nemoto
{"title":"Regulator of the Hesse cubic curves and hypergeometric functions","authors":"Yusuke Nemoto","doi":"10.1007/s00229-024-01587-7","DOIUrl":"https://doi.org/10.1007/s00229-024-01587-7","url":null,"abstract":"<p>We construct some integral elements in the motivic cohomology of the Hesse cubic curves and express their regulators in terms of generalized hypergeometric functions and Kampé de Fériet hypergeometric functions. By using these hypergeometric expressions, we obtain numerical examples of the Bloch-Beilinson conjecture on special values of <i>L</i>-functions.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":"143 1","pages":""},"PeriodicalIF":0.6,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141864397","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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