Regularized maximum of strictly plurisubharmonic functions on an almost complex manifold

TL;DR

This paper demonstrates that on an almost complex manifold, the maximum of two smooth strictly plurisubharmonic functions can be approximated uniformly by other smooth strictly plurisubharmonic functions, extending classical results.

Contribution

It introduces a method to approximate the maximum of two strictly plurisubharmonic functions with smooth ones on almost complex manifolds, a nontrivial extension of complex analysis techniques.

Findings

Maximum of two smooth strictly plurisubharmonic functions can be uniformly approximated by smooth strictly plurisubharmonic functions

Extension of classical complex analysis results to almost complex manifolds

Provides tools for potential theory on almost complex manifolds

Abstract

We prove that the maximum of two smooth strictly plurisubharmonic functions on an almost complex manifold can be uniformly approximated by smooth strictly plurisubharmonic functions.