# Regularity of envelopes in K\"ahler classes

## TL;DR

This paper proves that quasi-psh envelopes in a Kähler class are regularly smooth up to second derivatives, confirming a longstanding conjecture and advancing understanding of complex geometric structures.

## Contribution

It establishes the C^{1,1} regularity of quasi-psh envelopes in Kähler classes, confirming Berman's conjecture.

## Key findings

- Proves C^{1,1} regularity of quasi-psh envelopes
- Confirms a conjecture of Berman
- Advances understanding of Kähler geometry

## Abstract

We establish the C^{1,1} regularity of quasi-psh envelopes in a Kahler class, confirming a conjecture of Berman.