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)|
|Number of pages||62|
|Journal||Annales Scientifiques de l'Ecole Normale Superieure|
|State||Published - Nov 2006|
Bibliographical noteFunding Information:
1The first author was partially supported by NSF Grant DMS-0503735. 2The second author was partially supported by NSF Grant DMS-0404817.