Guan-Li type mean curvature flow for free boundary hypersurfaces in a ball
arXiv:1910.07253
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.
arXiv comment13 pages, final version, Comm. Anal. Geom., to appear