Li-Yau gradient estimates for curvature flows in positively curved manifolds

Paul Bryan, Heiko Kröner, Julian Scheuer

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We prove differential Harnack inequalities for flows of strictly convex hypersurfaces by powers p, 0<p<1, of the mean curvature in Einstein manifolds with a positive lower bound on the sectional curvature. We assume that this lower bound is sufficiently large compared to the derivatives of the curvature tensor of the ambient space and that the mean curvature of the initial hypersurface is sufficiently large compared to the ambient geometry. We also obtain some new Harnack inequalities for more general curvature flows in the sphere, as well as a monotonicity estimate for the mean curvature flow in non-negatively curved, locally symmetric spaces.
    Original languageEnglish
    JournalArxiv.org
    Publication statusSubmitted - 28 Jan 2019

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