Harnack estimate for mean curvature flow on the sphere

Paul Bryan, Mohammad N. Ivaki

    Research output: Contribution to journalArticle

    Abstract

    We consider the evolution of hypersurfaces on the unit sphere Sn+1 by their mean curvature. We prove a differential Harnack inequality for any weakly convex solution to the mean curvature flow. As an application, by applying an Aleksandrov reflection argument, we classify convex, ancient solutions of the mean curvature flow on the sphere. c 2020 International Press.

    Original languageEnglish
    Pages (from-to)165-176
    Number of pages12
    JournalAsian Journal of Mathematics
    Volume24
    Issue number1
    DOIs
    Publication statusPublished - Feb 2020

    Keywords

    • Mean curvature flow
    • Ancient solutions
    • Aleksandrov reflection
    • Harnack estimate

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