Communications in Analysis and Geometry

Volume 30 (2022)

Number 9

Guan–Li type mean curvature flow for free boundary hypersurfaces in a ball

Pages: 2157 – 2174

DOI: https://dx.doi.org/10.4310/CAG.2022.v30.n9.a8

Authors

Guofang Wang (Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Germany)

Chao Xia (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Abstract

In this paper we introduce a Guan–Li type volume preserving mean curvature flow for free boundary hypersurfaces in a ball. We give a concept of star-shaped free boundary hypersurfaces in a ball and show that the Guan–Li type mean curvature flow has long time existence and converges to a free boundary spherical cap, provided the initial data is star-shaped.

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G.W. is partly supported by Priority Programme “Geometry at Infinity” (SPP 2026) of DFG.

C.X. is supported by NSFC (Grant No. 11871406), by the Natural Science Foundation of Fujian Province of China (Grant No. 2017J06003), and by the Fundamental Research Funds for the Central Universities (Grant No. 20720180009).

Received 16 October 2019

Accepted 1 June 2020

Published 17 August 2023