MINKOWSKI INEQUALITY ON COMPLETE RIEMANNIAN WITH NONNEGATIVE RICCI CURVATURE

被引：2

作者：

Benatti, Luca ^{[1
]}

Fogagnolo, Mattia ^{[2
]}

Mazzieri, Lorenzo ^{[3
]}

机构：

[1] Univ Pisa, Pisa, Italy

[2] Univ Padua, Padua, Italy

[3] Univ Studi Trento, Povo, Italy

来源：

ANALYSIS & PDE | 2024年 / 17卷 / 09期

关键词：

geometric inequalities; nonlinear potential theory; monotonicity formulas; inverse mean curvature flow; REGULARITY; HYPERSURFACES; MONOTONICITY; GEOMETRY;

D O I：

10.2140/apde.2024.17.3039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider Riemannian manifolds of dimension at least 3, with nonnegative Ricci curvature and Euclidean volume growth. For every open bounded subset with smooth boundary we establish the validity of an optimal Minkowski inequality. We also characterise the equality case, provided the domain is strictly outward minimising and strictly mean convex. Along with the proof, we establish in full generality sharp monotonicity formulas, holding along the level sets of p-capacitary potentials in p-nonparabolic manifolds with nonnegative Ricci curvature.

引用

页码：3039 / 3077

页数：42

共 52 条

[1]

Agostiniani V., 2022, MATH ENG-US, V4, P13

[2] Minkowski Inequalities via Nonlinear Potential Theory [J].