# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1703.07727