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Eigenvalue Comparison on Bakry-Emery Manifolds

Andrews, Benjamin; Ni, Lei


We prove a comparison theorem on the modulus of continuity of the solution of a heat equation with a drifting term on Bakry-Emery manifolds. A direct consequence of the result is an alternate proof of an eigenvalue comparison result of Bakry-Qian. Examples are given to show that the estimate is sharp. Discussions on an explicit lower estimate for the corresponding ODE and an application to the diameter lower bound for gradient shrinking solitons are also included.

CollectionsANU Research Publications
Date published: 2012
Type: Journal article
Source: Communications in Partial Differential Equations
DOI: 10.1080/03605302.2012.668602


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