A mean curvature type flow in space forms

2013/09/19 by Guan, Pengfei, Li, Junfang · 5 citations
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1309.5099

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.

Cited by

• The quermassintegral inequalities for horo-convex domains in the sphere
• Evolution of hypersurfaces in (n+1)-dimensional light-cone
• On the new weighted geometric inequalities near the sphere in space forms
• A locally constrained inverse Hessian quotient flow in de Sitter space
• New weighted Alexandrov-Fenchel type inequalities and Minkowski inequalities in space forms

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