On the Compactness of Hamiltonian Stationary Lagrangian Surfaces in Kähler Surfaces

2019/10/06 by Jingyi Chen, Chen, Jingyi, John Man Shun Ma +1
Mathematics · #53D12 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1910.02549

openalex publication_date 2019/10/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a bubble tree convergence theorem for a sequence of closed Hamiltonian Stationary Lagrangian surfaces with bounded areas and Willmore energies in a complete Kähler surface. We also prove two strong compactness theorems on the space of Hamiltonian stationary Lagrangian tori in \mathbb C² and \mathbbCP² respectively.

Related

• Hamiltonian stationary Lagrangian surfaces in C²
• Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume
• The existence of Hamiltonian stationary Lagrangian tori in Kahler manifolds of any dimension
• Compactness of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds
• Hamiltonian Stationary Lagrangian Tori in Kaehler Manifolds