Hessian estimates for special Lagrangian equations with critical and supercritical phases in general dimensions

TL;DR

This paper establishes interior Hessian estimates for special Lagrangian equations with critical and supercritical phases across various dimensions, improving upon previous results especially in three-dimensional convex cases.

Contribution

The authors develop a unified method to derive sharper interior Hessian estimates for special Lagrangian equations in higher dimensions, extending known results.

Findings

Sharper interior Hessian estimates achieved in higher dimensions.

Unified approach applicable to critical and supercritical phases.

Improved results even for three-dimensional convex solutions.

Abstract

We derive a priori interior Hessian estimates for special Lagrangian equation with critical and supercritical phases in general higher dimensions. Our unified approach leads to sharper estimates even for the previously known three dimensional and convex solution cases.