## On short time existence for the planar network flow.(English)Zbl 1451.53121

Summary: 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.

### MSC:

 5.3e+11 Flows related to mean curvature 5.3e+100 Geometric evolution equations

### Keywords:

pseudolocality theorem; mean curvature flow
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