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arXiv · 1703.07493

Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds

Paul Bryan·Mohammad N. Ivaki·Julian Scheuer
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Abstract

We obtain Harnack estimates for a class of curvature flows in Riemannian manifolds of constant non-negative 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 manifold of non-negative sectional curvature. Using a concept of "duality" for strictly convex hypersurfaces, we also obtain a new type of inequalities, so-called "pseudo"-Harnack inequalities, for expanding flows in the sphere and in the hyperbolic space.

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Paul Bryan, Mohammad N. Ivaki, Julian Scheuer. 2017-03-22. Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds. https://doi.org/10.1515/crelle-2019-0006

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