Consequences of strong stability of minimal submanifolds

Author: 

Lotay, J
Schulze, F

Publication Date: 

April 2020

Journal: 

International Mathematics Research Notices

Last Updated: 

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

Issue: 

8

Volume: 

2020

DOI: 

10.1093/imrn/rny095

page: 

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.

Symplectic id: 

968679

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article