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.

Curvature evolution of nonconvex lens-shaped domains

NOVAGA, MATTEO
2011

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.
Bellettini, G; Novaga, Matteo
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11568/144426
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