The Neumann Problem of Complex Special Lagrangian Equations with Supercritical Phase

Abstract

Inspired by the Neumann problem of real special Lagrangian equations with supercritical phase, we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper, and establish the global C 2 estimates and the existence theorem by the method of continuity.

The Neumann problem for a type of fully nonlinear complex equations

“…Comparing to the complex fully nonlinear equations, the works about the real fully nonlinear equations are more abundant. We refer to [8,24,23,9,17,18,32,33,22,21,4,5,12,13,16] and references therein. We remark that in the above mentioned papers, the domain is assumed to be strictly pseudoconvex, convex or mean convex.…”