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

Bryan, Paul, Kröner, Heiko and Scheuer, Julian ORCID: https://orcid.org/0000-0003-2664-1896 2021. Li-Yau gradient estimates for curvature flows in positively curved manifolds. Methods and Applications of Analysis 27 (4) , pp. 341-358. 10.4310/MAA.2020.v27.n4.a2

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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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	International Press
ISSN:	1073-2772
Date of First Compliant Deposit:	14 October 2020
Date of Acceptance:	2 April 2020
Last Modified:	18 Nov 2024 08:45
URI:	https://orca.cardiff.ac.uk/id/eprint/135617

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