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Monge–Ampère equations and moduli spaces of manifolds of circular type by Giorgio Patrizio; Andrea Spiro is a Mathematics article available to read on EtoBox.

What is Monge–Ampère equations and moduli spaces of manifolds of circular type about?

A (bounded) manifold of circular type is a complex manifold M of dimension n admitting a (bounded) exhaustive real function u, defined on M minus a point x o , so that: (a) it is a smooth solution on M \ {x o } to the Monge-Ampère equation (dd c u) n = 0; (b) x o is a singular point for u of logarithmic type and e u extends smoothly on the blow up of M at x o ; (c) dd c (e u ) > 0 at any point of M \ {x o }. This class of manifolds naturally includes all smoothly bounded, strictly linearly convex domains and all smoothly bounded, strongly pseudoconvex circular domains of C n . A set of modular parameters for bounded manifolds of circular type is considered. In particular, for each biholomorphic equivalence class of them it is proved the existence of an essentially unique manifold in normal form. It is also shown that the class of normalizing maps for an n-dimensional manifold M is a new holomorphic invariant with the following property: it is parameterized by the points of a finite dimensional real manifold of dimension n 2 when M is a (non-convex) circular domain while it is of dimension n 2 + 2n when M is a strictly linearly convex domain. New characterizations of the circular do

Who reads Monge–Ampère equations and moduli spaces of manifolds of circular type?

Author

Giorgio Patrizio; Andrea Spiro

Publisher

Elsevier Science; Elsevier ; Elsevier Inc.; Elsevier BV (ISSN 0001-8708)

Published

2010

Language

EN

Field

Mathematics (Physical Sciences)