Singular Solutions to Special Lagrangian Equations with Subcritical Phases and Minimal Surface Systems

TL;DR

This paper constructs singular solutions for special Lagrangian equations with subcritical phases and minimal surface systems, and also produces families of solutions where a priori estimates break down.

Contribution

It introduces new singular solutions and demonstrates the failure of a priori estimates in specific cases of special Lagrangian equations.

Findings

Construction of singular solutions for subcritical phases

Families of solutions where a priori estimates break down

Extension of known a priori estimates to certain convex cases

Abstract

We construct singular solutions to special Lagrangian equa- tions with subcritical phases and minimal surface systems. A priori estimate breaking families of smooth solutions are also produced cor- respondingly. A priori estimates for special Lagrangian equations with certain convexity are largely known by now.