Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4606670 | Differential Geometry and its Applications | 2008 | 7 Pages |
Abstract
The purpose of this paper is to generalize the Liouville theorem for functions which are defined on the complete Riemannian manifolds. Then, we apply it to the isometric immersions between complete Riemannian manifolds in order to obtain an estimate for the size of the image of immersions in terms of the supremum of the length of their mean curvature vector in a quite general setting. The proofs are based on the Calabi's generalization of maximum principle for functions which are not necessarily differentiable.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Alireza Ranjbar-Motlagh,