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arXiv · 1802.03941

Consequences of strong stability of minimal submanifolds

Jason D. Lotay·Felix Schulze
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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.

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Jason D. Lotay, Felix Schulze. 2018-04-19. Consequences of strong stability of minimal submanifolds. https://doi.org/10.1093/imrn%2Frny095

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