Lagrangian F-stability of closed Lagrangian self-shrinkers

Abstract

In this paper, we study the Lagrangian F-stability of closed Lagrangian self-shrinkers immersed in complex Euclidean space. We show that any closed Lagrangian self-shrinker with first Betti number greater than one is Lagrangian F-unstable. In particular, any two-dimensional embedded closed Lagrangian self-shrinker is Lagrangian F-unstable. For a closed Lagrangian self-shrinker with first Betti number equal to one, we show that Lagrangian F-stability is equivalent to Hamiltonian F-stability. We also characterize Hamiltonian F-stability of a closed Lagrangian self-shrinker by its spectral property of the twisted Laplacian.

22 pages

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Cited by in corpus (3)

• Hamiltonian F-stability of complete Lagrangian self-shrinkers
• Hamiltonian L-stability of Lagrangian Translating Solitons
• Stabilities of homothetically shrinking Yang-Mills solitons