Modular data for Stein manifolds with special Monge-Ampère exhaustions (Q2909998)

The paper under review is the text of the conference given by the first author in Palermo at Convegno Internazionale di Geometria in honor of Renata Grimaldi on June 16, 2010.NEWLINENEWLINEThe paper contains a survey of recent results by the two authors. In particular, they outline the construction of modular data for a large class of complex manifolds. The class of complex manifolds which are considered here are the so-called manifolds of circular type, among which there are circular domains and bounded strictly convex domains. The authors illustrate how, extending and simplifying a construction due to Bland and Duchamp, the set of modular data of strictly convex domains introduced by Lempert describes exactly the class of manifolds of circular type.NEWLINENEWLINEThe paper ends with some applications and a section of open questions and possible directions of further research.