Optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds

TL;DR

This paper proves that the plurisubharmonic envelope of a $C^{1,1}$ function on a compact Hermitian manifold is $C^{1,1}$ regular and demonstrates that this regularity level is optimal through examples.

Contribution

It establishes the optimal regularity of plurisubharmonic envelopes on compact Hermitian manifolds, extending understanding of regularity in complex geometry.

Findings

Proves $C^{1,1}$ regularity of the envelope.

Provides examples showing the regularity is sharp.

Extends regularity results to Hermitian manifolds.

Abstract

In this paper, we prove the $C^{1, 1}$-regularity of the plurisubharmonic envelope of a $C^{1,1}$ function on a compact Hermitian manifold. We also present examples to show this regularity is sharp.