Eigenvalue Comparison on Bakry-Emery Manifolds

Ben Andrews, Lei Ni*

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    43 Citations (Scopus)

    Abstract

    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.

    Original languageEnglish
    Pages (from-to)2081-2092
    Number of pages12
    JournalCommunications in Partial Differential Equations
    Volume37
    Issue number11
    DOIs
    Publication statusPublished - Jan 2012

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