An energy gap phenomenon for the Whitney sphere

2019/10/04 by Liuyang Zhang, Zhang, Liuyang
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.01927

Abstract

For an immersed Lagrangian submanifold, let \checkA be the Lagrangian trace-free second fundamental form. In this note we consider the equation ∇^*T=0 on Lagrangian surfaces immersed in ℂ², where T=-2∇^*(\checkA\lrcornerω), and we prove a gap theorem for the Whitney sphere as a solution to this equation.

Citations

• Local Rigidity Theorems for Minimal Hypersurfaces

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