Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds

Paul Bryan, Mohammad N. Ivaki, Julian Scheuer

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1 Citation (Scopus)


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
Issue number764
Publication statusPublished - 2020


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