A mean curvature type flow in space forms

Academic Article

Abstract

  • © The Author(s) 2014. Published by Oxford University Press. All rights reserved. In this article, we introduce a new type of mean curvature flow (1.3) 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 ℝn+1, the quermassintegrals evolve monotonically along the flow which allows us to prove a class of Alexandrov-Fenchel inequalities of quermassintegrals.
  • Authors

    Digital Object Identifier (doi)

    Author List

  • Guan P; Li J
  • Start Page

  • 4716
  • End Page

  • 4740
  • Volume

  • 2015
  • Issue

  • 13