Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6416924 | Differential Geometry and its Applications | 2013 | 10 Pages |
Abstract
Given a positive function F on Sn which satisfies a convexity condition, for 1⩽r⩽n, we define for hypersurfaces in Rn+1 the r-th anisotropic mean curvature function Hr;F, a generalization of the usual r-th mean curvature function. We also define Lr;F operator, the linearized operator of the (r+1)-th anisotropic mean curvature, which is a generalization of the usual Lr operator for hypersurfaces in the Euclidean space Rn+1. The Reilly type inequalities for the first eigenvalue of the Lr;F operator have been proved.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yijun He,