Author

Arunima Bhattacharya

University of North Carolina, Chapel Hill

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Preprint Aug 2026

Nonuniqueness of solutions to the Lagrangian mean curvature equation

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 the unit ball with continuous boundary data. For every dimension $n\geq 2$, we construct a continuous phase $\psi \colon \overline{B_1}\to(-...

Arunima Bhattacharya, W. Ogden, Reese Harvey et al. · 0 citations

Preprint Aug 2026

Sharp partial regularity of Hamiltonian stationary and special Lagrangian graphs

We prove a sharp partial regularity result for Hamiltonian stationary Lagrangian Lipschitz submanifolds in arbitrary smooth almost K\"ahler manifolds: every weak solution of the corresponding equation is smooth away from a relatively closed singular set of Hausdorff dimension at most $n-5$. We show that the estimate is...

Arunima Bhattacharya, Gerard Orriols, A. Skorobogatova · 2 citations · ⚡1