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

Regularity properties of intrinsic objects for a large class of Stein Manifolds, namely of Monge–Ampère exhaustions and Kobayashi distance, are 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 C^n is also given. The research was partially supported by GNSAGA of INdAM