On short time existence for the planar network flow
Abstract
We prove the existence of the flow by curvature of regular planar networks starting from an initial network which is nonregular. 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.
 Publication:

arXiv eprints
 Pub Date:
 July 2014
 arXiv:
 arXiv:1407.4756
 Bibcode:
 2014arXiv1407.4756I
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematics  Differential Geometry
 EPrint:
 Final version, to appear in Journal of Differential Geometry. 51 pages