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Self-similarly expanding networks to curve shortening flow

Oliver C. Schnürer·Felix Schulze
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Abstract

We consider a network in the Euclidean plane that consists of three distinct half-lines with common start points. From that network as initial condition, there exists a network that consists of three curves that all start at one point, where they form 120 degree angles, and expands homothetically under curve shortening flow. We also prove uniqueness of these networks.

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Oliver C. Schnürer, Felix Schulze. 2007-02-23. Self-similarly expanding networks to curve shortening flow. https://arxiv.org/abs/math/0702698

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