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On short time existence for the planar network flow
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Ilmanen, Tom, Neves, André and Schulze, Felix (2019) On short time existence for the planar network flow. Journal of Differential Geometry, 111 (1). pp. 39-89. doi:10.4310/jdg/1547607687 ISSN 0022-040X.
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Official URL: http://dx.doi.org/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.
Item Type: | Journal Article | ||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Journal or Publication Title: | Journal of Differential Geometry | ||||||
Publisher: | Lehigh University * Department of Mathematics | ||||||
ISSN: | 0022-040X | ||||||
Official Date: | 16 January 2019 | ||||||
Dates: |
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Volume: | 111 | ||||||
Number: | 1 | ||||||
Page Range: | pp. 39-89 | ||||||
DOI: | 10.4310/jdg/1547607687 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Open Access Version: |
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