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.

7 pages, minor corrections. Final version to appear in IMRN

References in corpus (1)

• A strong stability condition on minimal submanifolds and its implications

Cited by in corpus (3)

• Graphical mean curvature flow with bounded bi-Ricci curvature
• $f$-minimal Lagrangian Submanifolds in Kähler Manifolds with Real Holomorphy Potentials
• Barrier methods for minimal submanifolds in the Gibbons-Hawking ansatz