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.
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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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