Regularity of Hamiltonian Stationary Equations in Symplectic manifolds

2021/07/31 by Arunima Bhattacharya, Jingyi Chen, Bhattacharya, Arunima +3 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2108.00325

openalex publication_date 2021/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove that any C¹-regular Hamiltonian stationary Lagrangian submanifold in a symplectic manifold is smooth. More broadly, we develop a regularity theory for a class of fourth order nonlinear elliptic equations with two distributional derivatives. Our fourth order regularity theory originates in the geometrically motivated variational problem for the volume functional, but should have applications beyond.

Cited by

• Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs

Related

• On the Regularity of Hamiltonian Stationary Lagrangian manifolds
• Regularity for Hamiltonian stationary equations in ℝ_{n≤ 4}ⁿ
• Generalizing symplectic topology from 1 to 2 dimensions
• Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
• Compactness of Hamiltonian stationary Lagrangian submanifolds in symplectic manifolds