On Non-Compact Complex Nil-Manifolds.
On proper R-actions on hyperbolic Stein surfaces.
On real submanifolds of and (Preliminary communication)
On regular Stein neighborhoods of a union of two totally real planes in ℂ²
We find regular Stein neighborhoods of a union of totally real planes M = (A+iI)ℝ² and N = ℝ² in ℂ², provided that the entries of a real 2 × 2 matrix A are sufficiently small. A key step in our proof is a local construction of a suitable function ρ near the origin. The sublevel sets of ρ are strongly Levi pseudoconvex and admit strong deformation retraction to M ∪ N.
On representation theory and the cohomology rings of irreducible compact hyperkähler manifolds of complex dimension four
In this paper, we continue the study of the possible cohomology rings of compact complex four dimensional irreducible hyperkähler manifolds. In particular, we prove that in the case b 2=7, b 3=0 or 8. The latter was achieved by the Beauville construction.
On Solvable Generalized Calabi-Yau Manifolds
We give an example of a compact 6-dimensional non-Kähler symplectic manifold that satisfies the Hard Lefschetz Condition. Moreover, it is showed that is a special generalized Calabi-Yau manifold.
On the approximation of functions on a Hodge manifold
If is a Hodge manifold and we construct a canonical sequence of functions such that in the topology. These functions have a simple geometric interpretation in terms of the moment map and they are real algebraic, in the sense that they are regular functions when is regarded as a real algebraic variety. The definition of is inspired by Berezin-Toeplitz quantization and by ideas of Donaldson. The proof follows quickly from known results of Fine, Liu and Ma.
On the automorphism group of strongly pseudoconvex domains in almost complex manifolds
In contrast with the integrable case there exist infinitely many non-integrable homogeneous almost complex manifolds which are strongly pseudoconvex at each boundary point. All such manifolds are equivalent to the Siegel half space endowed with some linear almost complex structure.We prove that there is no relatively compact strongly pseudoconvex representation of these manifolds. Finally we study the upper semi-continuity of the automorphism group of some hyperbolic strongly pseudoconvex almost...
On the Burns-Epstein invariants of spherical CR 3-manifolds
In this paper we develop a method to compute the Burns-Epstein invariant of a spherical CR homology sphere, up to an integer, from its holonomy representation. As an application, we give a formula for the Burns-Epstein invariant, modulo an integer, of a spherical CR structure on a Seifert fibered homology sphere in terms of its holonomy representation.
On the Calabi-Yau equation in the Kodaira-Thurston manifold
We review some previous results about the Calabi-Yau equation on the Kodaira-Thurston manifold equipped with an invariant almost-Kähler structure and assuming the volume form T2-invariant. In particular, we observe that under some restrictions the problem is reduced to aMonge-Ampère equation by using the ansatz ˜~ω = Ω− dJdu + da, where u is a T2-invariant function and a is a 1-form depending on u. Furthermore, we extend our analysis to non-invariant almost-complex structures by considering some...
On the compactification problem for Stein surfaces
On the -extension and the Hartogs extension
On the embedding and compactification of -complete manifolds
We characterize intrinsically two classes of manifolds that can be properly embedded into spaces of the form . The first theorem is a compactification theorem for pseudoconcave manifolds that can be realized as where is a projective variety. The second theorem is an embedding theorem for holomorphically convex manifolds into .
On the embedding of 1-convex manifolds with 1-dimensional exceptional sets.
On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics
On the Homotopy Groups of Complex Projective Algebraic Manifolds.
On the Homotopy Groups of Complex Projective Algebraic Manifolds.
On the Kählerian geometry of 1-convex threefolds.
On the Minimal Models of Complex Manifolds.