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Partial regularity for minimizers of a class of discontinuous Lagrangians 一类不连续拉格朗日最小值的部分正则性
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-14 DOI: 10.1007/s00229-024-01547-1
Roberto Colombo
{"title":"Partial regularity for minimizers of a class of discontinuous Lagrangians","authors":"Roberto Colombo","doi":"10.1007/s00229-024-01547-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01547-1","url":null,"abstract":"<p>We study a one-dimensional Lagrangian problem including the variational reformulation, derived in a recent work of Ambrosio–Baradat–Brenier, of the discrete Monge–Ampère gravitational model, which describes the motion of interacting particles whose dynamics is ruled by the optimal transport problem. The more general action-type functional we consider contains a discontinuous potential term related to the descending slope of the opposite squared distance function from a generic discrete set in <span>(mathbb {R}^{d})</span>. We exploit the underlying geometrical structure provided by the associated Voronoi decomposition of the space to obtain <span>(C^{1,1})</span>-regularity for local minimizers out of a finite number of shock times.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152648","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
Hodge numbers of O’Grady 6 via Ngô strings 奥格雷迪的霍奇数 6 通过 Ngô 字符串
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01540-8
Ben Wu
{"title":"Hodge numbers of O’Grady 6 via Ngô strings","authors":"Ben Wu","doi":"10.1007/s00229-024-01540-8","DOIUrl":"https://doi.org/10.1007/s00229-024-01540-8","url":null,"abstract":"<p>We give an alternative computation of the Betti and Hodge numbers for manifolds of <i>OG</i>6 type using the method of Ngô Strings introduced by de Cataldo, Rapagnetta, and Saccà.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152735","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
Poisson commutative subalgebras associated with a Cartan subalgebra 与 Cartan 子代数相关的泊松交换子代数
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-13 DOI: 10.1007/s00229-024-01545-3
Oksana S. Yakimova
{"title":"Poisson commutative subalgebras associated with a Cartan subalgebra","authors":"Oksana S. Yakimova","doi":"10.1007/s00229-024-01545-3","DOIUrl":"https://doi.org/10.1007/s00229-024-01545-3","url":null,"abstract":"<p>Let <span>({mathfrak g})</span> be a reductive Lie algebra and <span>(mathfrak tsubset mathfrak g)</span> a Cartan subalgebra. The <span>(mathfrak t)</span>-stable decomposition <span>({mathfrak g}=mathfrak toplus {mathfrak m})</span> yields a bi-grading of the symmetric algebra <span>({mathcal {S}}({mathfrak g}))</span>. The subalgebra <span>({mathcal {Z}}_{({mathfrak g},mathfrak t)})</span> generated by the bi-homogenous components of the symmetric invariants <span>(Fin {mathcal {S}}({mathfrak g})^{mathfrak g})</span> is known to be Poisson commutative. Furthermore the algebra <span>({tilde{{mathcal {Z}}}}=textsf{alg}langle {mathcal {Z}}_{({mathfrak g},{mathfrak t})},{mathfrak t}rangle )</span> is also Poisson commutative. We investigate relations between <span>({tilde{{mathcal {Z}}}})</span> and Mishchenko–Fomenko subalgebras. In type <span>A</span>, we construct a quantisation of <span>({tilde{{mathcal {Z}}}})</span> making use of quantum Mishchenko–Fomenko algebras.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140152982","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
Weights for compact connected Lie groups 紧凑相连李群的权重
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-09 DOI: 10.1007/s00229-024-01538-2
Radha Kessar, Gunter Malle, Jason Semeraro
{"title":"Weights for compact connected Lie groups","authors":"Radha Kessar, Gunter Malle, Jason Semeraro","doi":"10.1007/s00229-024-01538-2","DOIUrl":"https://doi.org/10.1007/s00229-024-01538-2","url":null,"abstract":"<p>Let <span>(ell )</span> be a prime. If <span>(textbf{G})</span> is a compact connected Lie group, or a connected reductive algebraic group in characteristic different from <span>(ell )</span>, and <span>(ell )</span> is a good prime for <span>(textbf{G})</span>, we show that the number of weights of the <span>(ell )</span>-fusion system of <span>(textbf{G})</span> is equal to the number of irreducible characters of its Weyl group. The proof relies on the classification of <span>(ell )</span>-stubborn subgroups in compact Lie groups.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140105436","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
Upper bounds for the critical values of homology classes of loops 循环同构类临界值的上限
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-02 DOI: 10.1007/s00229-024-01541-7
Hans-Bert Rademacher
{"title":"Upper bounds for the critical values of homology classes of loops","authors":"Hans-Bert Rademacher","doi":"10.1007/s00229-024-01541-7","DOIUrl":"https://doi.org/10.1007/s00229-024-01541-7","url":null,"abstract":"<p>In this short note we discuss upper bounds for the critical values of homology classes in the based and free loop space of compact manifolds carrying a Riemannian or Finsler metric of positive Ricci curvature. In particular it follows that a shortest closed geodesic on a compact and simply-connected <i>n</i>-dimensional manifold of positive Ricci curvature <span>(text {Ric}ge n-1)</span> has length <span>(le n pi .)</span> This improves the bound <span>(8pi (n-1))</span> given by Rotman (Positive Ricci curvature and the length of a shortest periodic geodesic. arXiv:2203.09492, 2022).</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018846","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
Diameter estimates for surfaces in conformally flat spaces 共形平面空间中曲面的直径估计值
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-01 DOI: 10.1007/s00229-024-01539-1
Marco Flaim, Christian Scharrer
{"title":"Diameter estimates for surfaces in conformally flat spaces","authors":"Marco Flaim, Christian Scharrer","doi":"10.1007/s00229-024-01539-1","DOIUrl":"https://doi.org/10.1007/s00229-024-01539-1","url":null,"abstract":"<p>The aim of this paper is to give an upper bound for the intrinsic diameter of a surface with boundary immersed in a conformally flat three dimensional Riemannian manifold in terms of the integral of the mean curvature and of the length of its boundary. Of particular interest is the application of the inequality to minimal surfaces in the three-sphere and in the hyperbolic space. Here the result implies an a priori estimate for connected solutions of Plateau’s problem, as well as a necessary condition on the boundary data for the existence of such solutions. The proof follows a construction of Miura and uses a diameter bound for closed surfaces obtained by Topping and Wu–Zheng.</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140018869","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
Sign-changing solution for logarithmic elliptic equations with critical exponent 有临界指数的对数椭圆方程的符号变化解法
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-03-01 DOI: 10.1007/s00229-024-01535-5
Tianhao Liu, Wenming Zou
{"title":"Sign-changing solution for logarithmic elliptic equations with critical exponent","authors":"Tianhao Liu, Wenming Zou","doi":"10.1007/s00229-024-01535-5","DOIUrl":"https://doi.org/10.1007/s00229-024-01535-5","url":null,"abstract":"<p>In this paper, we consider the logarithmic elliptic equations with critical exponent </p><span>$$begin{aligned} left{ begin{array}{ll} -Delta u=lambda u+ |u|^{2^*-2}u+theta ulog u^2, u in H_0^1(Omega ), quad Omega subset {{mathbb {R}}}^N. end{array}right. end{aligned}$$</span><p>Here, the parameters <span>(Nge 6)</span>, <span>(lambda in {{mathbb {R}}})</span>, <span>(theta &gt;0)</span> and <span>( 2^*=frac{2N}{N-2} )</span> is the Sobolev critical exponent. We prove the existence of a sign-changing solution with exactly two nodal domain for an arbitrary smooth bounded domain <span>(Omega subset {mathbb {R}}^{N})</span>. When <span>(Omega =B_R(0))</span> is a ball, we also construct infinitely many radial sign-changing solutions with alternating signs and prescribed nodal characteristic.\u0000</p>","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140886552","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
An improvement of the Myers theorem 迈尔斯定理的改进
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-02-29 DOI: 10.1007/s00229-024-01534-6
Murat Limoncu
{"title":"An improvement of the Myers theorem","authors":"Murat Limoncu","doi":"10.1007/s00229-024-01534-6","DOIUrl":"https://doi.org/10.1007/s00229-024-01534-6","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140413205","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
From Milnor number to the Euler obstruction of a map on isolated determinantal singularities 从米尔诺数到孤立行列式奇点上映射的欧拉阻塞
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-02-12 DOI: 10.1007/s00229-023-01528-w
Raphael de Omena, N. Grulha, Miriam S. Pereira
{"title":"From Milnor number to the Euler obstruction of a map on isolated determinantal singularities","authors":"Raphael de Omena, N. Grulha, Miriam S. Pereira","doi":"10.1007/s00229-023-01528-w","DOIUrl":"https://doi.org/10.1007/s00229-023-01528-w","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139842421","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
From Milnor number to the Euler obstruction of a map on isolated determinantal singularities 从米尔诺数到孤立行列式奇点上映射的欧拉阻塞
IF 0.6 4区 数学
Manuscripta Mathematica Pub Date : 2024-02-12 DOI: 10.1007/s00229-023-01528-w
Raphael de Omena, N. Grulha, Miriam S. Pereira
{"title":"From Milnor number to the Euler obstruction of a map on isolated determinantal singularities","authors":"Raphael de Omena, N. Grulha, Miriam S. Pereira","doi":"10.1007/s00229-023-01528-w","DOIUrl":"https://doi.org/10.1007/s00229-023-01528-w","url":null,"abstract":"","PeriodicalId":49887,"journal":{"name":"Manuscripta Mathematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2024-02-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139782689","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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