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Remarks on the self-shrinking Clifford torus
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Evans, Christopher G., Lotay, Jason D. and Schulze, Felix (2020) Remarks on the self-shrinking Clifford torus. Journal fur die reine und angewandte Mathematik (Crelles Journal), 2020 (765). pp. 139-170. doi:10.1515/crelle-2019-0015 ISSN 0075-4102.
An open access version can be found in:
Official URL: http://dx.doi.org/10.1515/crelle-2019-0015
Abstract
On the one hand, we prove that the Clifford torus in C2 is unstable for Lagrangian mean curvature flow under arbitrarily small Hamiltonian perturbations, even though it is Hamiltonian F-stable and locally area minimising under Hamiltonian variations. On the other hand, we show that the Clifford torus is rigid: it is locally unique as a self-shrinker for mean curvature flow, despite having infinitesimal deformations which do not arise from rigid motions. The proofs rely on analysing higher order phenomena: specifically, showing that the Clifford torus is not a local entropy minimiser even under Hamiltonian variations, and demonstrating that infinitesimal deformations which do not generate rigid motions are genuinely obstructed.
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 August 2020 | ||||||||
Dates: |
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Volume: | 2020 | ||||||||
Number: | 765 | ||||||||
Page Range: | pp. 139-170 | ||||||||
DOI: | 10.1515/crelle-2019-0015 | ||||||||
Status: | Peer Reviewed | ||||||||
Publication Status: | Published | ||||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||||
Open Access Version: |
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