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Consequences of strong stability of minimal submanifolds

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arxiv 1802.03941 v2 pith:KIEWMAYO submitted 2018-02-12 math.DG math.AP

Jason D. Lotay , Felix Schulze This is my paper · ORCID
classification math.DGmath.AP
keywords minimalsubmanifoldsflowresultstabilitystablestronglyamongst
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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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