# On short time existence for the planar network flow

@article{Ilmanen2019OnST, title={On short time existence for the planar network flow}, author={Tom Ilmanen and Andre' Neves and Felix Schulze}, journal={Journal of Differential Geometry}, year={2019} }

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…

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