Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4669329 | Bulletin des Sciences Mathématiques | 2006 | 7 Pages |
Abstract
In this paper, we study the volume growth property of a non-compact complete Riemannian manifold M. We improve the volume growth theorem of Calabi (1975) and Yau (1976), Cheeger, Gromov and Taylor (1982). Then we use our new result to study gradient Ricci solitons. We also show that on M, for any q∈(0,∞), every non-negative Lq subharmonic function is constant under a natural decay condition on the Ricci curvature.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)