Comparison geometry for the bakry-emery ricci tensor

Guofang Wei, Will Wylie

Research output: Contribution to journalArticle

250 Scopus citations

Abstract

For Riemannian manifolds with a measure (M, g, e−fdvolg) we prove mean curvature and volume comparison results when the∞- Bakry-Emery Ricci tensor is bounded from below and f or |∇f| is bounded, generalizing the classical ones (i.e. when f is constant). This leads to extensions of many theorems for Ricci curvature bounded below to the Bakry-Emery Ricci tensor. In particular, we give extensions of all of the major comparison theorems when f is bounded. Simple examples show the bound on f is necessary for these results.

Original languageEnglish (US)
Pages (from-to)337-405
Number of pages69
JournalJournal of Differential Geometry
Volume83
Issue number2
DOIs
StatePublished - Jan 1 2009
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory
  • Geometry and Topology

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