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arXiv · 0906.0166

Curvature Evolution of Nonconvex Lens-Shaped Domains

G. Bellettini·M. Novaga
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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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G. Bellettini, M. Novaga. 2009-05-31. Curvature Evolution of Nonconvex Lens-Shaped Domains. https://arxiv.org/abs/0906.0166

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