Consequences of strong stability of minimal submanifolds
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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2018
- DOI:
- 10.48550/arXiv.1802.03941
- arXiv:
- arXiv:1802.03941
- Bibcode:
- 2018arXiv180203941L
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Analysis of PDEs
- E-Print:
- 7 pages, minor corrections. Final version to appear in IMRN