Semi-convex viscosity solutions of the special Lagrangian equation
Analysis of PDEs
2025-10-21 v1 Differential Geometry
Abstract
We prove smoothness and interior derivative estimates for viscosity solutions to the special Lagrangian equation with almost negative phases and small enough semi-convexity. We show by example that the range of phases we consider and the semi-convexity condition are sharp. As an application, we find a new Liouville theorem for entire such solutions of the special Lagrangian equation with subcritical phase. We also find effective Hessian estimates with exponential dependence, which we show to be optimal.
Keywords
Cite
@article{arxiv.2510.17202,
title = {Semi-convex viscosity solutions of the special Lagrangian equation},
author = {Connor Mooney and Ravi Shankar},
journal= {arXiv preprint arXiv:2510.17202},
year = {2025}
}