17 citations · 49 across the 24 of their papers we have counts for
25 papers
Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs
Arunima Bhattacharya, Gerard Orriols, Anna Skorobogatova
We prove a sharp partial regularity result for Hamiltonian stationary Lagrangian Lipschitz submanifolds in arbitrary smooth almost Kähler manifolds: every weak solution of the corr…
Nonuniqueness of solutions to the Lagrangian mean curvature equation
Arunima Bhattacharya, W. Jacob Ogden
We resolve a question posed by Harvey and Lawson concerning the uniqueness of continuous viscosity solutions to the Dirichlet problem for the Lagrangian mean curvature equation on…
Optimal Transport and Generalized Lagrangian Mean Curvature Flows on Kim-McCann Metrics
Arunima Bhattacharya, Micah Warren, Daniel Weser
We express the mean curvature flow of Lagrangian submanifolds in pseudo-Riemannian manifolds endowed with the Kim-McCann-Warren metric within the framework of generalized mean curv…
Doubling and the two-dimensional critical valued Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall
In this paper, we establish interior Hessian and gradient estimates for the two-dimensional Lagrangian mean curvature equation when the phase changes signs, provided the gradient o…
Optimal Regularity for Hölder continuous Hamiltonian Stationary Lagrangian graphs
Arunima Bhattacharya, W. Jacob Ogden
In this paper, we establish optimal regularity for Hölder continuous Hamiltonian stationary Lagrangian graphs in . We prove that such a graph is smooth whenever its H…
Singularities of the Lagrangian mean curvature flow at the critical Lagrangian phase
Arunima Bhattacharya, Ravi Shankar, Jeremy Wall +1
We establish interior estimates for singularities of the Lagrangian mean curvature flow when the Lagrangian phase is critical, i.e., , and extend our resul…
Regularity for Hamiltonian stationary equations in
Arunima Bhattacharya
In this paper, we study the regularity of solutions to the Hamiltonian stationary equation in complex Euclidean space. We show that in dimensions , for all values of the L…
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 Priori Estimates for Singularities of the Lagrangian Mean Curvature Flow with Supercritical Phase
Arunima Bhattacharya, Jeremy Wall
In this paper, we prove interior a priori estimates for singularities of the Lagrangian mean curvature flow assuming the Lagrangian phase is supercritical. We prove a Jacobi inequa…
Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian Mean Curvature Flow
Arunima Bhattacharya, Jeremy Wall
In this paper, we prove interior Hessian estimates for shrinkers, expanders, translators, and rotators of the Lagrangian mean curvature flow under the assumption that the Lagrangia…
The CR-Volume of Horizontal Submanifolds of Spheres
Jacob Bernstein, Arunima Bhattacharya
We study an analog in CR-geometry of the conformal volume of Li-Yau. In particular, to submanifolds of odd-dimensional spheres that are Legendrian or, more generally, horizontal wi…
Minimal surfaces and Colding-Minicozzi entropy in complex hyperbolic space
Jacob Bernstein, Arunima Bhattacharya
We study notions of asymptotic regularity for a class of minimal submanifolds of complex hyperbolic space that includes minimal Lagrangian submanifolds. As an application, we show…
Variational integrals on Hessian spaces: partial regularity for critical points
Arunima Bhattacharya, Anna Skorobogatova
We develop regularity theory for critical points of variational integrals defined on Hessian spaces of functions on open, bounded subdomains of , under compactly supp…
Colding-Minicozzi Entropies in Cartan-Hadamard Manifolds
Jacob Bernstein, Arunima Bhattacharya
We introduce a family of functionals on submanifolds of Cartan-Hadamard manifolds that generalize the Colding-Minicozzi entropy of submanifolds of Euclidean space. We show that the…
Gradient estimates for the Lagrangian mean curvature equation with critical and supercritical phase
Arunima Bhattacharya, Connor Mooney, Ravi Shankar
In this paper, we prove interior gradient estimates for the Lagrangian mean curvature equation, if the Lagrangian phase is critical and supercritical and . Combined with the…
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…
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…
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…
Optimal regularity for Lagrangian mean curvature type equations
Arunima Bhattacharya, Ravi Shankar
We classify regularity for Lagrangian mean curvature type equations, which include the potential equation for prescribed Lagrangian mean curvature and those for Lagrangian mean cur…
Regularity for convex viscosity solutions of Lagrangian mean curvature equation
Arunima Bhattacharya, Ravi Shankar
We show that convex viscosity solutions of the Lagrangian mean curvature equation are regular if the Lagrangian phase has Hölder continuous second derivatives.
Hessian Estimates for Lagrangian mean curvature equation
Arunima Bhattacharya
In this paper, we derive a priori interior Hessian estimates for Lagrangian mean curvature equation if the Lagrangian phase is supercritical and has bounded second derivatives.
The Dirichlet problem for Lagrangian mean curvature equation
Arunima Bhattacharya
In this paper, we solve the Dirichlet problem with continuous boundary data for the Lagrangian mean curvature equation on a uniformly convex, bounded domain in .
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…
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…