Work

Comparison geometry for the Bakry-Emery Ricci tensor

Year: 2009

Type: article

Abstract: For Riemannian manifolds with a measure (M, g, e -f dvol g ) 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.

Source: Journal of Differential Geometry

DOI: 10.4310/jdg/1261495336

Authors: Guofang Wei, Will Wylie

Institutions: University of California, Santa Barbara, University of Pennsylvania, University of California, Los Angeles

Language: English

Topic: Geometric Analysis and Curvature Flows

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Problems Related to Ricci Curvature