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Harnack inequalities for evolving hypersurfaces on the sphere

Harnack inequalities for evolving hypersurfaces on the sphere

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 ≤ 1.If f is the mean curvature, we obtain stronger Harnack inequalities.