Mathematics > Differential Geometry
[Submitted on 31 Jul 2021
]
Title: Regularity of Hamiltonian Stationary Equations in Symplectic manifolds
Title: 哈密顿平稳方程在辛流形中的正则性
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.
Submission history
From: Arunima Bhattacharya [view email][v1] Sat, 31 Jul 2021 21:32:11 UTC (307 KB)
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