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arXiv · 0711.1108

Evolution of convex lens-shaped networks under curve shortening flow

Oliver C. Schnürer·Abderrahim Azouani·Marc Georgi·Juliette Hell·Nihar Jangle·Amos Koeller·Tobias Marxen·Sandra Ritthaler·Mariel Sáez·Felix Schulze·Brian Smith
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Abstract

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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Oliver C. Schnürer, Abderrahim Azouani, Marc Georgi, Juliette Hell, Nihar Jangle, Amos Koeller, Tobias Marxen, Sandra Ritthaler, Mariel Sáez, Felix Schulze, Brian Smith. 2007-11-07. Evolution of convex lens-shaped networks under curve shortening flow. https://arxiv.org/abs/0711.1108

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