Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant nonnegative sectional curvature as well as in the Lorentzian Minkowski and de Sitter spaces. Furthermore, we prove a Harnack estimate with a bonus term for mean curvature flow in locally symmetric Riemannian Einstein manifolds of nonnegative sectional curvature. Using a concept of "duality" for strictly convex hypersurfaces, we also obtain a new type of inequality, so-called "pseudo"-Harnack inequality, for expanding flows in the sphere and in the hyperbolic space.

    Original languageEnglish
    Pages (from-to)71-109
    Number of pages39
    JournalJournal fur die Reine und Angewandte Mathematik
    Volume2020
    Issue number764
    DOIs
    Publication statusPublished - 2020

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