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arXiv · 1309.5099

A mean curvature type flow in space forms

Pengfei Guan·Junfang Li
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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.

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Pengfei Guan, Junfang Li. 2013-09-19. A mean curvature type flow in space forms. https://arxiv.org/abs/1309.5099

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