具有中间里奇曲率下限的流形中迈克尔-西蒙-索博廖夫不等式的最优传输方法

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2023-12-13 DOI:10.1007/s10455-023-09934-9

Kai-Hsiang Wang

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引用次数: 0

摘要

我们将麦肯的最优传输定理推广到子流形环境中，并用它证明了流形中具有中间利玛窦曲率下限的子流形的迈克尔-西蒙-索博廖夫不等式。这些结果包括布伦德尔（arXiv:2009.13717）的尖锐迈克尔-西蒙-索博廖夫不等式在中间利玛窦曲率为非负时的变体。

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Optimal transport approach to Michael–Simon–Sobolev inequalities in manifolds with intermediate Ricci curvature lower bounds

We generalize McCann’s theorem of optimal transport to a submanifold setting and use it to prove Michael–Simon–Sobolev inequalities for submanifolds in manifolds with lower bounds on intermediate Ricci curvatures. The results include a variant of the sharp Michael–Simon–Sobolev inequality in Brendle’s (arXiv:2009.13717) when the intermediate Ricci curvatures are nonnegative.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.