The Clifford torus as a self-shrinker for the Lagrangian mean curvature flow

Abstract

We provide several rigidity results for the Clifford torus in the class of compact self-shrinkers for Lagrangian mean curvature flow.

arXiv comment10 pages

References in corpus (7)

• Volume growth, eigenvalue and compactness for self-shrinkers
• Homology class of a Lagrangian Klein bottle
• Recent Progress on Singularities of Lagrangian Mean Curvature Flow
• Hamiltonian stationary self-similar solutions for Lagrangian mean curvature flow in complex Euclidean plane
• The rigidity theorems of self shrinkers
• Classification and rigidity of self-shrinkers in the Mean curvature flow
• Complete self-shrinkers of the mean curvature flow

Cited by in corpus (4)

• Lagrangian F-stability of closed Lagrangian self-shrinkers
• Hamiltonian F-stability of complete Lagrangian self-shrinkers
• On the rigidity theorems for Lagrangian translating solitons in pseudo-Euclidean space II
• Closed Lagrangian self-shrinkers in ${\mathbb{R}}^4$ symmetric with respect to a hyperplane