3 papers
math.AP2026
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…
math.AP2025
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…
math.DG2024
Grim Raindrop: A Translating Solution to Curve Diffusion Flow
W. Jacob Ogden, Micah Warren
We show the existence of a properly immersed translating solution to curve diffusion flow in the plane. Curve diffusion flow is a higher order version of curve shortening flow, nam…