Abstract
We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincaré inequality. In the process, a sharp decay estimate for the minimal positive Green's function is obtained. This estimate only depends on the weight function of the Poincaré inequality, and yields a criterion of parabolicity of connected components at infinity in terms of the weight function.
Original language | English (US) |
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Pages (from-to) | 921-982 |
Number of pages | 62 |
Journal | Annales Scientifiques de l'Ecole Normale Superieure |
Volume | 39 |
Issue number | 6 |
DOIs | |
State | Published - Nov 2006 |
Bibliographical note
Funding Information:1The first author was partially supported by NSF Grant DMS-0503735. 2The second author was partially supported by NSF Grant DMS-0404817.