A note on exhaustion of hyperbolic complex manifolds

0 A note on extended complex manifolds

We introduce a category of extended complex manifolds, and prove that the func-tor describing deformations of a classical compact complex manifold M within this category is versally representable by (an analytic subspace in) H * (M, T M). By restricting the associated versal family of extended complex manifolds over H * (M, T M) to the subspace H 1 (M, T M) one gets a correct limit to the class...

A Note on Homogeneous Complex Contact Manifolds

A Mass for Asymptotically Complex Hyperbolic Manifolds

We prove a positive mass theorem for complete Kähler manifolds that are asymptotic to the complex hyperbolic space.

Cohomologically Hyperbolic Endomorphisms of Complex Manifolds

We show that if a compact Kähler manifold X admits a cohomologically hyperbolic surjective endomorphism then its Kodaira dimension is non-positive. This gives an affirmative answer to a conjecture of Guedj in the holomorphic case. The main part of the paper is to determine the geometric structure and the fundamental groups (up to finite index) for those X of dimension 3.

On asymmetric hyperbolic manifolds

We show that for every n ≥ 2 there exists closed hyperbolic n-manifolds for which the full group of orientation preserving isometries is trivial. 2000 Mathematics Subject Classification 57S25, 57N16