Regularity of Hamiltonian Stationary Equations in Symplectic manifolds
Differential Geometry
2021-08-03 v1 Analysis of PDEs
Abstract
In this paper, we prove that any -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.
Keywords
Cite
@article{arxiv.2108.00325,
title = {Regularity of Hamiltonian Stationary Equations in Symplectic manifolds},
author = {Arunima Bhattacharya and Jingyi Chen and Micah Warren},
journal= {arXiv preprint arXiv:2108.00325},
year = {2021}
}