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Evolution of convex lens-shaped networks under curve shortening flow

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arxiv 0711.1108 v1 pith:IWBHJPDV submitted 2007-11-07 math.DG math.AP

Oliver C. Schnürer , Abderrahim Azouani , Marc Georgi , Juliette Hell , Nihar Jangle , Amos Koeller , Tobias Marxen , Sandra Ritthaler
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Mariel Sáez Felix Schulze Brian Smith (for the Lens Seminar)
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classification math.DGmath.AP
keywords networksconvexappropriatecurveflowlens-shapedself-similarlyshortening
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We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.

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