Harnack inequalities for curvature flows depending on mean curvature
- authored by
- Knut Smoczyk
- Abstract
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 = Aαx α with two constants A and α.
- External Organisation(s)
-
ETH Zurich
- Type
- Article
- Journal
- New York journal of mathematics
- Volume
- 3
- Pages
- 103-118
- No. of pages
- 16
- ISSN
- 1076-9803
- Publication date
- 21.11.1997
- Publication status
- Published
- Peer reviewed
- Yes
- ASJC Scopus subject areas
- General Mathematics
