Modular data and regularity of Monge-Ampère exhaustions and of Kobayashi distance

Abstract

Regularity properties of intrinsic objects for a large class of Stein Manifolds, namely of Monge-Ampère exhaustions and Kobayashi distance, is interpreted in terms of modular data. The results lead to a construction of an infinite dimensional family of convex domains with squared Kobayashi distance of prescribed regularity properties. A new sharp refinement of Stoll's characterization of ${\mathbb{C}}^n$ is also given.

arXiv comment25 pages