Dilation Type Inequalities for Strongly-Convex Sets in Weighted Riemannian Manifolds

IF 0.9 3区数学 Q2 MATHEMATICS Analysis and Geometry in Metric Spaces Pub Date : 2021-01-01 DOI:10.1515/agms-2020-0128

Hiroshi Tsuji

引用次数: 1

Abstract

Abstract In this paper, we consider a dilation type inequality on a weighted Riemannian manifold, which is classically known as Borell’s lemma in high-dimensional convex geometry. We investigate the dilation type inequality as an isoperimetric type inequality by introducing the dilation profile and estimate it by the one for the corresponding model space under lower weighted Ricci curvature bounds. We also explore functional inequalities derived from the comparison of the dilation profiles under the nonnegative weighted Ricci curvature. In particular, we show several functional inequalities related to various entropies.

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加权黎曼流形中强凸集的扩张型不等式

摘要在本文中，我们考虑了加权黎曼流形上的一个扩张型不等式，它在高维凸几何中被称为Borell引理。通过引入扩张轮廓，我们将扩张型不等式研究为等周型不等式，并通过在较低加权Ricci曲率边界下对相应模型空间的扩张轮廓进行估计。我们还探讨了在非负加权Ricci曲率下，从膨胀轮廓的比较中导出的函数不等式。特别地，我们展示了几个与各种熵相关的函数不等式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.

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