Regularity of rooftop envelopes

Abstract

We study continuity, Hölder 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.

25 pages. We removed Section 3.2 in the previous version since the non-compact version of Edwards' theorem has some issues