Curvature Evolution of Nonconvex Lens-Shaped Domains

Details Curvature Evolution of Nonconvex Lens-Shaped Domains Curvature Evolution of Nonconvex Lens-Shaped Domains

2009-05-31

arxiv.org/abs/0906.0166v1

Mathematics

Differential Geometry

25 pages, 7 figures

Scientific paper

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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