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January 2019 On short time existence for the planar network flow
Tom Ilmanen, André Neves, Felix Schulze
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J. Differential Geom. 111(1): 39-89 (January 2019). DOI: 10.4310/jdg/1547607687

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. "On short time existence for the planar network flow." J. Differential Geom. 111 (1) 39 - 89, January 2019. https://doi.org/10.4310/jdg/1547607687

Information

Received: 30 June 2015; Published: January 2019
First available in Project Euclid: 16 January 2019

zbMATH: 07004531
MathSciNet: MR3909904
Digital Object Identifier: 10.4310/jdg/1547607687

Rights: Copyright © 2019 Lehigh University

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Vol.111 • No. 1 • January 2019
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