Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds

Bryan, Paul, Ivaki, Mohammad N. and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 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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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.

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:	06 Dec 2024 11:00
URI:	https://orca.cardiff.ac.uk/id/eprint/131157

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