Evans, CG;
Lotay, JD;
Schulze, F;
(2020)
Remarks on the self-shrinking Clifford torus.
Journal für die reine und angewandte Mathematik
, 2020
(765)
pp. 139-170.
10.1515/crelle-2019-0015.
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Abstract
On the one hand, we prove that the Clifford torus in C^{2} 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.
| Type: | Article |
|---|---|
| Title: | Remarks on the self-shrinking Clifford torus |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1515/crelle-2019-0015 |
| Publisher version: | https://doi.org/10.1515/crelle-2019-0015 |
| 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/10073301 |
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