A Mean Curvature Type Flow in Space Forms

By Pengfei Guan, Junfang Li. 2013

142 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0a69edf65a6ed1300826cedbf397dbdfe74e3e8e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Yong Wei
2. Haizhong Li
3. Yingxiang Hu
4. Ben Andrews

In Geometry and Topology

1. Yong Wei
2. Haizhong Li
3. Yingxiang Hu
4. Ben Andrews

Citations in the corpus

• Locally constrained curvature flows and geometric inequalities in hyperbolic space (2020, methodology): “We remark that the idea of using Minkowski (type) formula to define locally constrained curvature flows has been explored by Guan, Li and Wang [14,16] in space forms and certain warped product spaces.”