$\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow

Abstract

In this paper, we formulate the notion of the $\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\mathcal{F}$-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's results.

23 pages

References in corpus (1)

• Evolution of curves and surfaces by mean curvature

Cited by in corpus (5)

• Eigenvalues of the drifted Laplacian on complete metric measure spaces
• Lagrangian F-stability of closed Lagrangian self-shrinkers
• Classification and rigidity of self-shrinkers in the Mean curvature flow
• Hamiltonian F-stability of complete Lagrangian self-shrinkers
• Stabilities of homothetically shrinking Yang-Mills solitons