7 citations · 33 across the 19 of their papers we have counts for
20 papers
A Liouville type theorem for ancient Lagrangian mean curvature flows
Arunima Bhattacharya, Micah Warren, Daniel Weser
We prove a Liouville type result for convex solutions of the Lagrangian mean curvature flow with restricted quadratic growth assumptions at antiquity on the solutions.
A Geometric flow towards hamiltonian stationary submanifolds
Jingyi Chen, Micah Warren
In this paper, we introduce a geometric flow for Lagrangian submanifolds in a Kähler manifold that stays in its initial Hamiltonian isotopy class and is a gradient flow for volume.…
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…
estimates for solutions to almost linear elliptic equations
Arunima Bhattacharya, Micah Warren
In this paper, we show interior estimates for viscosity solutions of fully non-linear, uniformly elliptic equations, which are close to linear equations and we also compu…
Compactification of the space of Hamiltonian stationary Lagrangian submanifolds with bounded total extrinsic curvature and volume
Jingyi Chen, Micah Warren
For a sequence of immersed connected closed Hamiltonian stationary Lagrangian submaniolds in with uniform bounds on their volumes and the total extrinsic curvature…
Interior Schauder estimates for the fourth order Hamiltonian stationary equation in two dimensions
Arunima Bhattacharya, Micah Warren
We consider the Hamiltonian stationary equation for all phases in dimension two. We show that solutions that are will be smooth and we also derive a estimate fo…