Inverse Gauss curvature flows with free boundaries in a cone
Differential Geometry
2020-08-10 v2 Analysis of PDEs
Abstract
We consider strictly convex hypersurfaces with the boundary which meets a strictly convex cone perpendicularly. We prove that if these hypersurfaces expand inside this cone, driven by the power of the Gauss curvature, then the evolution exists for all the time and the evolving hypersurfaces converge smoothly to a piece of round sphere after rescaling.
Keywords
Cite
@article{arxiv.1802.05413,
title = {Inverse Gauss curvature flows with free boundaries in a cone},
author = {Li Chen and Ni Xiang},
journal= {arXiv preprint arXiv:1802.05413},
year = {2020}
}
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31 pages