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arXiv · 1312.4771

Lagrangian F-stability of closed Lagrangian self-shrinkers

Jiayu Li·Yongbing Zhang
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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.

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Jiayu Li, Yongbing Zhang. 2013-12-17. Lagrangian F-stability of closed Lagrangian self-shrinkers. https://arxiv.org/abs/1312.4771

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