Willmore Flow of Complete Surfaces
Differential Geometry
2024-01-25 v1
Abstract
We consider the Willmore flow equation for complete, properly immersed surfaces in Rn. Given bounded geometry on the initial surface, we extend the result by Kuwert and Sch\"atzle in 2002 and prove short time existence and uniqueness of the Willmore flow. We also show that a complete Willmore surface with low Willmore energy must be a plane, and that a Willmore flow with low initial energy and Euclidean volume growth must converge smoothly to a plane.
Cite
@article{arxiv.2212.08692,
title = {Willmore Flow of Complete Surfaces},
author = {Long-Sin Li},
journal= {arXiv preprint arXiv:2212.08692},
year = {2024}
}
Comments
47 pages