April 5, 2008 (Saturday)
Room 517, Meng Wah
Complex, HKU
Professor Giorgio Patrizio
Università degli
Deformations of CR structures, moduli
and normal forms for manifolds with special Monge-Ampère
exhaustions
Abstract
We study the
problem of determining the moduli space for a class
of complex manifolds which include naturally all the smoothly bounded, strictly
linearly convex domains and all smoothly bounded, strongly pseudoconvex
circular domains in Cn. In
particular, for each biholomorphic equivalence class
of them it is proved that there exists an essentially unique manifold in normal
form and the class of normalizing maps is parametrized.
The results complete and systematize earlier work of Lempert
and Bland-Duchamp.