Communications in Analysis and Geometry

Volume 26 (2018)

Number 5

Harnack inequalities for evolving hypersurfaces on the sphere

Pages: 1047 – 1077



Paul Bryan (Department of Mathematics, Macquarie University, Sydney, NSW, Australia)

Mohammad N. Ivaki (Department of Mathematics, University of Toronto, Ontario, Canada)

Julian Scheuer (Mathematisches Institut, Albert-Ludwigs-Universität, Freiburg, Germany)


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

Received 11 December 2015

Published 3 January 2019