On short time existence for the planar network flow
Analysis of PDEs
2018-02-21 v2 Differential Geometry
Abstract
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is non-regular. The proof relies on a monotonicity formula for expanding solutions and a local regularity result for the network flow in the spirit of B. White's local regularity theorem for mean curvature flow. We also show a pseudolocality theorem for mean curvature flow in any codimension, assuming only that the initial submanifold can be locally written as a graph with sufficiently small Lipschitz constant.
Cite
@article{arxiv.1407.4756,
title = {On short time existence for the planar network flow},
author = {Tom Ilmanen and André Neves and Felix Schulze},
journal= {arXiv preprint arXiv:1407.4756},
year = {2018}
}
Comments
Final version, to appear in Journal of Differential Geometry. 51 pages