A priori interior estimates for special Lagrangian curvature equations

TL;DR

This paper derives interior curvature and gradient estimates for special Lagrangian curvature equations, advancing understanding of their geometric properties in critical and convex cases.

Contribution

It provides new a priori interior estimates for the curvature and gradients of solutions to special Lagrangian equations, covering critical phase and convex scenarios.

Findings

Established interior curvature estimates in critical phase and convex case.

Proved interior gradient estimates for any constant phase.

Enhanced theoretical understanding of special Lagrangian curvature equations.

Abstract

We establish a priori interior curvature estimates for the special Lagrangian curvature equations in both the critical phase and convex case. Additionally, we prove a priori interior gradient estimates for any constant phases.