Doubling Argument of the Hessian Estimate for the Special Lagrangian Equation on General Phases with Constraints

TL;DR

This paper introduces a new doubling argument technique to derive Hessian estimates for the special Lagrangian equation with general phase constraints, bypassing traditional inequalities and establishing related geometric theorems.

Contribution

The paper presents a novel doubling argument method for Hessian estimates in special Lagrangian equations under general phases, independent of the Michael-Simon inequality.

Findings

Hessian estimates for special Lagrangian equations established

Doubling argument method developed

Alexandrov-type theorems proved

Abstract

In this paper, we establish a doubling argument to obtain Hessian estimates for the special Lagrangian equation under general phase constraints. In particular, our approach does not rely on the Michael-Simon mean value inequality. As an intermediate step, we also establish Alexandrov-type theorems, which may be of independent interest.