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Journal Article

Self similar expanding solutions of the planar network flow

MPS-Authors

Saez,  Mariel
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

0704.3113v1.pdf
(Preprint), 178KB

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Citation

Mazzeo, R., & Saez, M. (n.d.). Self similar expanding solutions of the planar network flow.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-5FC1-6
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 Schn\"urer 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 $t=0$.