Details
| Original language | English |
|---|---|
| Pages (from-to) | 103-118 |
| Number of pages | 16 |
| Journal | New York journal of mathematics |
| Volume | 3 |
| Publication status | Published - 21 Nov 1997 |
| Externally published | Yes |
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.
Keywords
- Curvature, Flow, Harnack, Mean, Selfsimilar
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: New York journal of mathematics, Vol. 3, 21.11.1997, p. 103-118.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Harnack inequalities for curvature flows depending on mean curvature
AU - Smoczyk, Knut
PY - 1997/11/21
Y1 - 1997/11/21
N2 - 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.
AB - 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.
KW - Curvature
KW - Flow
KW - Harnack
KW - Mean
KW - Selfsimilar
UR - http://www.scopus.com/inward/record.url?scp=3042559710&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:3042559710
VL - 3
SP - 103
EP - 118
JO - New York journal of mathematics
JF - New York journal of mathematics
SN - 1076-9803
ER -