Integral formulas for the -equation on complex projective algebraic manifolds
Integral formulas on projective space and the radon transform of Gindikin-Henkin-Polyakov.
We construct a variant of Koppelman's formula for (0,q)-forms with values in a line bundle, O(l), on projective space. The formula is then applied to a study of a Radon transform for (0,q)-forms, introduced by Gindikin-Henkin-Polyakov. Our presentation follows along the basic lines of Henkin-Polyakov [3], with some simplifications.
Invariance of cohomological q-completeness under finite holomorphic surjections.
Kählerian extensions of the symplectic reduction.
Kantenkohomologie
Lefschetzsätze und Hyperkonvexität.
Local q-completeness of complements of smooth CR-submanifolds.
Modulräume holomorpher Abbildungen auf konkaven komplexen Räumen
n-Concavity of n-dimensional complex spaces.
Non-embeddable -convex manifolds
We show that every small resolution of a 3-dimensional terminal hypersurface singularity can occur on a non-embeddable -convex manifold.We give an explicit example of a non-embeddable manifold containing an irreducible exceptional rational curve with normal bundle of type . To this end we study small resolutions of -singularities.
Oka' s inequality for currents and applications.
On Grauert's conjecture and the characterization of Moishezon spaces.
On -Runge pairs
We show that the converse of the aproximation theorem of Andreotti and Grauert does not hold. More precisely we construct a -complete open subset (which is an analytic complement in the unit ball) such that the restriction map has a dense image for every but the pair is not a -Runge pair.
On Strict Levi q-Convexity and q-Concavity on Domains with Piecewise Smooth Boundaries.
On Strongly Pseudo-convex Kähler Manifolds.
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 embedding of 1-convex manifolds with 1-dimensional exceptional set
In this paper we show that a 1-convex (i.e., strongly pseudoconvex) manifold , with 1- dimensional exceptional set and finitely generated second homology group , is embeddable in if and only if is Kähler, and this case occurs only when does not contain any effective curve which is a boundary.
On the homology groups of -complete spaces
On the Kählerian geometry of 1-convex threefolds.