Curvature Evolution of Nonconvex Lens-Shaped Domains
Differential Geometry
2009-06-02 v1 Analysis of PDEs
Abstract
We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point. Our theorem is the analog of the result of Grayson for curvature flow of closed planar embedded curves.
Keywords
Cite
@article{arxiv.0906.0166,
title = {Curvature Evolution of Nonconvex Lens-Shaped Domains},
author = {G. Bellettini and M. Novaga},
journal= {arXiv preprint arXiv:0906.0166},
year = {2009}
}
Comments
25 pages, 7 figures