Weighted Poincaré inequality and rigidity of complete manifolds

Details Weighted Poincaré inequality and rigidity of complete manifolds Weighted Poincaré inequality and rigidity of complete manifolds

2007-01-24

arxiv.org/abs/math/0701693v2

Mathematics

Differential Geometry

Scientific paper

We prove structure theorems for complete manifolds satisfying both the Ricci curvature lower bound and the weighted Poincar\'e 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 Poincar\'e inequality, and yields a criterion of parabolicity of connected components at infinity in terms of the weight function.

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