Oka' s inequality for currents and applications.
On a Minimal Complex Norm that Extends the Real Euclidean Norm.
On Bergman completeness of pseudoconvex Reinhardt domains
On extremal holomorphically contractible families
We prove (Theorem 1.2) that the category of generalized holomorphically contractible families (Definition 1.1) has maximal and minimal objects. Moreover, we present basic properties of these extremal families.
On extremal mappings in complex ellipsoids
Using a generalization of [Pol] we present a description of complex geodesics in arbitrary complex ellipsoids.
On Grauert's conjecture and the characterization of Moishezon spaces.
On holomorphic isometries for the Kobayashi and Carathéodory distances on complex manifolds
It is shown that under certain conditions every holomorphic isometry for the Carathéodory or the Kobayashi distances is an isometry for the corrisponding metrics. These results are used to give a characterization of biholomorphic mappings between convex domains and complete circular domains.
On holomorphic maps between domains in
On horospheres and holomorphic endomorfisms of the Siegel disc
On hulls of meromorphy and a class of Stein manifolds
On isometries of the carathéodory and Kobayashi metrics on strongly pseudoconvex domains
Let and be domains in and an isometry for the Kobayashi or Carathéodory metrics. Suppose that extends as a map to . We then prove that is a CR or anti-CR diffeomorphism. It follows that and must be biholomorphic or anti-biholomorphic.
On isometries of the Kobayashi and Carathéodory metrics
This article considers C¹-smooth isometries of the Kobayashi and Carathéodory metrics on domains in ℂⁿ and the extent to which they behave like holomorphic mappings. First we provide an example which suggests that 𝔹ⁿ cannot be mapped isometrically onto a product domain. In addition, we prove several results on continuous extension of C⁰-isometries f : D₁ → D₂ to the closures under purely local assumptions on the boundaries. As an application, we show that there is no C⁰-isometry between a strongly...
On iterates of holomorphic maps.
On Lempert functions in .
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 symmetry of the pluricomplex Green function for ellipsoids
We show that in the class of complex ellipsoids the symmetry of the pluricomplex Green function is equivalent to convexity of the ellipsoid.
On the Bergman distance on model domains in ℂⁿ
Let P be a real-valued and weighted homogeneous plurisubharmonic polynomial in and let D denote the “model domain” z ∈ ℂⁿ | r(z):= Re z₁ + P(z’) < 0. We prove a lower estimate on the Bergman distance of D if P is assumed to be strongly plurisubharmonic away from the coordinate axes.
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 .