# Consequences of strong stability of minimal submanifolds

Lotay, J
Schulze, F

April 2020

## Journal:

International Mathematics Research Notices

## Last Updated:

2021-08-08T09:57:13.363+01:00

8

2020

## DOI:

10.1093/imrn/rny095

2352-2360

## 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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