Curvature Evolution of Nonconvex Lens-Shaped Domains
arXiv:0906.0166
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.
25 pages, 7 figures