Details
| Original language | English |
|---|---|
| Pages (from-to) | 225-236 |
| Number of pages | 12 |
| Journal | Manuscripta mathematica |
| Volume | 95 |
| Issue number | 2 |
| Publication status | Published - 1 Feb 1998 |
| Externally published | Yes |
Abstract
Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds that are close to them. This gives a classification of the possible singularities for these surfaces in the case n = 2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity occurs.
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
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In: Manuscripta mathematica, Vol. 95, No. 2, 01.02.1998, p. 225-236.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Starshaped hypersurfaces and the mean curvature flow
AU - Smoczyk, Knut
PY - 1998/2/1
Y1 - 1998/2/1
N2 - Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds that are close to them. This gives a classification of the possible singularities for these surfaces in the case n = 2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity occurs.
AB - Under the assumption of two a-priori bounds for the mean curvature, we are able to generalize a recent result due to Huisken and Sinestrari [8], valid for mean convex surfaces, to a much larger class. In particular we will demonstrate that these a-priori bounds are satisfied for a class of surfaces including meanconvex as well as starshaped surfaces and a variety of manifolds that are close to them. This gives a classification of the possible singularities for these surfaces in the case n = 2. In addition we prove that under certain initial conditions some of them become mean convex before the first singularity occurs.
UR - http://www.scopus.com/inward/record.url?scp=0031987423&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0031987423
VL - 95
SP - 225
EP - 236
JO - Manuscripta mathematica
JF - Manuscripta mathematica
SN - 0025-2611
IS - 2
ER -