A mean curvature type flow in space forms
Differential Geometry
2013-09-23 v1 Analysis of PDEs
Abstract
In this article, we introduce a new type of mean curvature flow for bounded star-shaped domains in space forms and prove its longtime existence, exponential convergence without any curvature assumption. Along this flow, the enclosed volume is a constant and the surface area evolves monotonically. Moreover, for a bounded convex domain in R n+1, the quermassintegrals evolve monotonically along the flow which allows us to prove a class of Alexandrov-Fenchel inequalities of quermassintegrals.
Cite
@article{arxiv.1309.5099,
title = {A mean curvature type flow in space forms},
author = {Pengfei Guan and Junfang Li},
journal= {arXiv preprint arXiv:1309.5099},
year = {2013}
}