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Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds

Bryan, Paul, Ivaki, Mohammad N. and Scheuer, Julian 2020. Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds. Journal für die reine und angewandte Mathematik 2020 (764) , pp. 71-109. 10.1515/crelle-2019-0006

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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.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: De Gruyter
ISSN: 0075-4102
Date of First Compliant Deposit: 21 April 2020
Date of Acceptance: 18 April 2019
Last Modified: 07 Jan 2021 12:30

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