Hamiltonian F-stability of complete Lagrangian self-shrinkers

Abstract

In this paper, we study the Lagrangian F-stability and Hamiltonian F-stability of Lagrangian self-shrinkers. We prove a characterization theorem for the Hamiltonian F-stability of $n$-dimensional complete Lagrangian self-shrinkers without boundary, with polynomial volume growth and with the second fundamental form satisfying the condition that there exist constants $C_0>0$ and $\epsilon <\frac{1}{16n}$ such that $|A{|}^2\le C_0+\epsilon |x{|}^2$. We characterize the Hamiltonian F-stablity by the eigenvalues and eigenspaces of the drifted Laplacian.

v1: 20 pages; v2: 21 pages, we weakened our condition on the second fundamental norm in this version; v3: 21 pages, revised (9.17), and corresponding minor changes in the last section

References in corpus (5)

• The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow
• Uniqueness of blowups and Lojasiewicz inequalities
• $\mathcal{F}$-stability for self-shrinking solutions to mean curvature flow
• Lagrangian F-stability of closed Lagrangian self-shrinkers
• The Stability of Self-Shrinkers of Mean Curvature Flow in Higher Codimension

Cited by in corpus (1)

• Hamiltonian L-stability of Lagrangian Translating Solitons