New York Journal of Mathematics
Volume 3 (1997) 103-118


Knut Smoczyk

Harnack Inequalities For Curvature Flows Depending On Mean Curvature

Published: November 21, 1997
Keywords: Harnack, mean, curvature, flow, selfsimilar
Subject: 53C21 (35K15)

We prove Harnack inequalities for parabolic flows of compact orientable hypersurfaces in Rn+1, where the normal velocity is given by a smooth function f depending only on the mean curvature. We use these estimates to prove longtime existence of solutions in some highly nonlinear cases. In addition we prove that compact selfsimilar solutions with constant mean curvature must be spheres and that compact selfsimilar solutions with nonconstant mean curvature can only occur in the case, where f=Aαxα with two constants A and α.

Author information

ETH Zürich, Math. Department, CH-8092 Zürich, Switzerland