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arXiv · 0704.3113

Self similar expanding solutions of the planar network flow

Rafe Mazzeo·Mariel Saez
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Abstract

We prove the existence of self-similar expanding solutions of the curvature flow on planar networks where the initial configuration is any number of half-lines meeting at the origin. This generalizes recent work by Schnürer and Schulze which treats the case of three half-lines. There are multiple solutions, and these are parametrized by combinatorial objects, namely Steiner trees with respect to a complete negatively curved metric on the unit ball which span $k$ specified points on the boundary at infinity. We also provide a sharp formulation of the regularity of these solutions at $t=0$.

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Rafe Mazzeo, Mariel Saez. 2007-04-24. Self similar expanding solutions of the planar network flow. https://arxiv.org/abs/0704.3113

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