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.
Bellettini, G., Novaga, M. (2011). Curvature evolution of nonconvex lens-shaped domains. JOURNAL FÜR DIE REINE UND ANGEWANDTE MATHEMATIK, 656, 17-46 [10.1515/CRELLE.2011.041].
Curvature evolution of nonconvex lens-shaped domains
Bellettini, Giovanni;
2011-01-01
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.
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https://hdl.handle.net/11365/1017454