On Compact Riemannian Manifolds with Convex Boundary and Ricci Curvature Bounded from Below

被引：3

作者：

Wang, Xiaodong ^{[1
]}

机构：

[1] Michigan State Univ, Dept Math, E Lansing, MI 48824 USA

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2021年 / 31卷 / 04期

关键词：

Ricci curvature; Harmonic functions; Rigidity; EMBEDDED MINIMAL-SURFACES; SOBOLEV INEQUALITIES; RIGIDITY; SPHERES;

D O I：

10.1007/s12220-020-00422-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We propose to study positive harmonic functions satisfying a nonlinear Neuman condition on a compact Riemannian manifold with nonnegative Ricci curvature and strictly convex boundary. A precise conjecture is formulated. We discuss its implications and present some partial results. Related questions are discussed for compact Riemannian manifolds with positive Ricci curvature and convex boundary.

引用

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页码：3988 / 4003

页数：16

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