Weighted Poincaré inequality and rigidity of complete manifolds

Peter Li, Jiaping Wang

Research output: Contribution to journalArticlepeer-review

68 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 languageEnglish (US)
Pages (from-to)921-982
Number of pages62
JournalAnnales Scientifiques de l'Ecole Normale Superieure
Volume39
Issue number6
DOIs
StatePublished - 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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