Harnack inequalities for evolving hypersurfaces on the sphere

Abstract

We prove Harnack inequalities for hypersurfaces flowing on the unit sphere by $p$-powers of a strictly monotone, 1-homogeneous, convex, curvature function $f$, $0<p\le 1.$ If $f$ is the mean curvature, we obtain stronger Harnack inequalities.

22 pages; Thoroughly revised version. We improved the main theorem a bit

Cited by in corpus (3)

• Inverse curvature flows in Riemannian warped products
• On the classification of ancient solutions to curvature flows on the sphere
• Harnack inequalities for curvature flows in Riemannian and Lorentzian manifolds