Gaussian Curvature Estimates for the Convex Level Sets of p-Harmonic Functions

被引：39

作者：

Ma, Xi-Nan ^{[1
]}

Ou, Qianzhong ^{[2
]}

Zhang, Wei ^{[1
]}

机构：

[1] Univ Sci & Technol China, Dept Math, Hefei 230026, Anhui, Peoples R China

[2] Hezhou Univ, Dept Math, Hezhou 542800, Guangxi Prov, Peoples R China

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2010年 / 63卷 / 07期

基金：

美国国家科学基金会;

关键词：

ELLIPTIC-EQUATIONS; PARALLEL PLANES; SURFACES; CURVES; RINGS;

D O I：

10.1002/cpa.20318

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We give a positive lower bound for the Gaussian curvature of the convex level sets of p-harmonic functions with the Gaussian curvature of the boundary and the norm of the gradient on the boundary. Combining the deformation process, this estimate gives a new approach to studying the convexity of the level sets of the p-harmonic function. (C) 2010 Wiley Periodicals, Inc.

引用

页码：935 / 971

页数：37

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