Regularity of the plurisubharmonic envelope in strictly pseudoconvex domains

TL;DR

This paper investigates the regularity properties of plurisubharmonic envelopes within smooth strictly pseudoconvex domains in complex space, establishing a complex analogue of a known optimal regularity result.

Contribution

It extends the regularity results of plurisubharmonic envelopes to the setting of smooth strictly pseudoconvex domains, providing a complex analogue of a classical real-variable theorem.

Findings

Proves optimal regularity of plurisubharmonic envelopes in strictly pseudoconvex domains

Establishes a complex analogue of De Philippis and Figalli's result

Enhances understanding of complex potential theory in pseudoconvex domains

Abstract

We study the plurisubharmonic envelopes of functions in the setting of domains in $\mathbb C^n$. In particular we prove a complex analogue of a result of De Philippis and Figalli concerning the optimal regularity of such envelopes in smooth strictly pseudoconvex domains.