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A local regularity theorem for mean curvature flow with triple edges

Schulze, F; White, B; (2020) A local regularity theorem for mean curvature flow with triple edges. Journal für die reine und angewandte Mathematik (Crelles Journal) , 2020 (758) 10.1515/crelle-2017-0044. Green open access

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Abstract

Mean curvature flow of clusters of n-dimensional surfaces in Rn+k 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.

Type: Article
Title: A local regularity theorem for mean curvature flow with triple edges
Open access status: An open access version is available from UCL Discovery
DOI: 10.1515/crelle-2017-0044
Publisher version: http://dx.doi.org/10.1515/crelle-2017-0044
Language: English
Additional information: This version is the version of record. For information on re-use, please refer to the publisher’s terms and conditions.
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/1571171
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