Reflection Principle for the Complex Monge\u2013Amp\xe8re Equation and Plurisubharmonic Functions

Abstract

We study reflection principle for several central objects in pluripotential theory. First we show that the odd reflected function gives an extension for pluriharmonic functions over a flat boundary. Then we show that the even reflected function gives an extension for nonnegative plurisubharmonic functions. In particular cases odd and/or even reflected functions give extensions for classical solutions of the homogeneous complex Monge–Ampère equation. Finally, we state reflection principle for the generalized complex Monge–Ampère equation and maximal plurisubharmonic functions.