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A local regularity theorem for mean curvature flow with triple edges
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Schulze, Felix and White, Brian (2020) A local regularity theorem for mean curvature flow with triple edges. Journal fur die reine und angewandte Mathematik (Crelles Journal), 2020 (758). pp. 281-305. doi:10.1515/crelle-2017-0044 ISSN 0075-4102.
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Official URL: http://dx.doi.org/10.1515/crelle-2017-0044
Abstract
Mean curvature flow of clusters of n-dimensional surfaces in [Math Processing Error] that meet in triples at equal angles along smooth edges and higher order junctions on lower-dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smooth mean curvature flow with triple edges is weakly close to a static union of three n-dimensional unit density half-planes, then it is smoothly close. Extending the regularity result to a class of integral Brakke flows, we show that this implies smooth short-time existence of the flow starting from an initial surface cluster that has triple edges, but no higher order junctions.
Item Type: | Journal Article | ||||||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||||
Journal or Publication Title: | Journal fur die reine und angewandte Mathematik (Crelles Journal) | ||||||||
Publisher: | Walter de Gruyter GmbH & Co. KG | ||||||||
ISSN: | 0075-4102 | ||||||||
Official Date: | 1 January 2020 | ||||||||
Dates: |
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Volume: | 2020 | ||||||||
Number: | 758 | ||||||||
Page Range: | pp. 281-305 | ||||||||
DOI: | 10.1515/crelle-2017-0044 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access |
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