Regularity of rooftop envelopes

TL;DR

This paper investigates the regularity properties of geodesics and rooftop envelopes of continuous plurisubharmonic functions in complex analysis, focusing on continuity, Hölder, and $C^{1,1}$ regularity.

Contribution

It establishes new regularity results for rooftop envelopes and geodesics between continuous plurisubharmonic functions in complex domains.

Findings

Proves continuity and Hölder regularity of geodesics.

Establishes $C^{1,1}$-regularity under certain conditions.

Derives regularity properties of rooftop envelopes.

Abstract

We study continuity, H\"older regularity, and $C^{1,1}$-regularity of geodesics between continuous plurisubharmonic functions on bounded domains of $\mathbb{C}^n$. We then derive regularity properties of rooftop envelopes.