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arXiv · 1407.4756

On short time existence for the planar network flow

Tom Ilmanen·André Neves·Felix Schulze
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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.

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Tom Ilmanen, André Neves, Felix Schulze. 2014-07-17. On short time existence for the planar network flow. https://arxiv.org/abs/1407.4756

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