Starshaped hypersurfaces and the mean curvature flow

verfasst von

Knut Smoczyk

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.

Externe Organisation(en)

ETH Zürich

Typ

Artikel

Journal

Manuscripta mathematica

Band

95

Seiten

225-236

Anzahl der Seiten

12

ISSN

0025-2611

Publikationsdatum

01.02.1998

Publikationsstatus

Veröffentlicht

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Allgemeine Mathematik