Regularity of Hamiltonian Stationary Equations in Symplectic manifolds

Arunima Bhattacharya; Jingyi Chen; Micah Warren

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arXiv · 2108.00325

Regularity of Hamiltonian Stationary Equations in Symplectic manifolds

Arunima Bhattacharya·Jingyi Chen·Micah Warren

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Abstract

In this paper, we prove that any $C^{1}$-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.

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Arunima Bhattacharya, Jingyi Chen, Micah Warren. 2021-07-31. Regularity of Hamiltonian Stationary Equations in Symplectic manifolds. https://arxiv.org/abs/2108.00325

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