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 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 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 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 Geodesics of the Bergman Metric.
On the Geometry of Moduli Spaces.
On the Green function on a certain class of hyperconvex domains
We study the behavior of the pluricomplex Green function on a bounded hyperconvex domain D that admits a smooth plurisubharmonic exhaustion function ψ such that 1/|ψ| is integrable near the boundary of D, and moreover satisfies the estimate at points close enough to the boundary with constants C,C’ > 0 and 0 < α < 1. Furthermore, we obtain a Hopf lemma for such a function ψ. Finally, we prove a lower bound on the Bergman distance on D.
On the Hausdorff measures associated to the Carathéodory and Kobayashi metrics
On the Kähler form of the moduli space of once punctured tori.
On the Kobayashi and Caratheodory pseudometric reductions of homogeneous complex spaces
On the Kobayashi metric for perturbations of the ball.