Self similar expanding solutions of the planar network flow
| dc.creator | Mazzeo, Rafe | |
| dc.creator | Saez, Mariel | |
| dc.date | 2007-04-24 | |
| dc.date.accessioned | 2026-07-07T07:57:56Z | |
| dc.date.available | 2026-07-07T07:57:56Z | |
| dc.description | 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 $t=0$. | |
| dc.description | 14 pages | |
| dc.identifier | https://arxiv.org/abs/0704.3113 | |
| dc.identifier | http://arxiv.org/abs/0704.3113 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/127829 | |
| dc.subject | Differential Geometry | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 53C44 | |
| dc.title | Self similar expanding solutions of the planar network flow | |
| dc.type | text |