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math.AP2021★ 8 cited
A note on the two dimensional Lagrangian mean curvature equation
Arunima Bhattacharya
In this note, we use Warren-Yuan's super isoperimetric inequality on the level sets of subharmonic functions, which is available only in two dimensions, to derive a modified Hessia…
math.AP2021
Regularity for critical points of convex functionals on Hessian spaces
Arunima Bhattacharya
We consider variational integrals of the form where is convex and smooth on the Hessian space. We show that a critical point of such a functi…
math.DG2021
Regularity of Hamiltonian Stationary Equations in Symplectic manifolds
Arunima Bhattacharya, Jingyi Chen, Micah Warren
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…