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Consequences of strong stability of minimal submanifolds

Lotay, JD; Schulze, F; (2020) Consequences of strong stability of minimal submanifolds. International Mathematics Research Notices , 2020 (8) pp. 2352-2360. 10.1093/imrn/rny095. Green open access

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Abstract

In this note we show that the recent dynamical stability result for small $C^1$-perturbations of strongly stable minimal submanifolds of C.-J. Tsai and M.-T. Wang directly extends to the enhanced Brakke flows of Ilmanen. We illustrate applications of this result, including a local uniqueness statement for strongly stable minimal submanifolds amongst stationary varifolds, and a mechanism to flow through some singularities of Lagrangian mean curvature flow which are proved to occur by Neves.

Type: Article
Title: Consequences of strong stability of minimal submanifolds
Open access status: An open access version is available from UCL Discovery
DOI: 10.1093/imrn/rny095
Publisher version: https://doi.org/10.1093/imrn/rny095
Language: English
Additional information: This version is the author accepted manuscript. 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/10047158
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