Weighted Poincaré inequality and rigidity of complete manifolds

Peter Li; Jiaping Wang

doi:10.1016/j.ansens.2006.11.001

Weighted Poincaré inequality and rigidity of complete manifolds

Peter Li
, Jiaping Wang

School of Mathematics

Research output: Contribution to journal › Article › peer-review

103 Scopus citations

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)
Pages (from-to)	921-982
Number of pages	62
Journal	Annales Scientifiques de l'Ecole Normale Superieure
Volume	39
Issue number	6
DOIs	https://doi.org/10.1016/j.ansens.2006.11.001
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.

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10.1016/j.ansens.2006.11.001

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abstract = "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.",

author = "Peter Li and Jiaping Wang",

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.",

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N2 - 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.

AB - 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.

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M3 - Article

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SN - 0012-9593

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ER -

Weighted Poincaré inequality and rigidity of complete manifolds

Abstract

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