Quantitative Quermassintegral Inequalities for Nearly Spherical Sets

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2022-01-12 DOI:10.1142/s0219199723500268

Caroline VanBlargan, Yi Wang

引用次数: 3

Abstract

In this paper, we establish quantitative Alexandrov-Fenchel inequalities for quermassintegrals on nearly spherical sets. In particular, we bound the $(k,m)$-isoperimetric deficit from below by the Frankael asymmetry. We also find a lower bound on the $(k,m)$-isoperimetric deficit using the spherical deviation.

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近球集的定量Quermassintegral不等式

本文建立了近球集上quermass积分的定量Alexandrov-Fenchel不等式。特别地，我们从下面用Frankael不对称约束了$(k,m)$-等周赤字。我们还利用球面偏差找到了$(k,m)$-等周亏缺的下界。

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

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.