On values of homogeneous polynomials in discrete sets of points
Operator theory and the Carathéodory metric.
Parabolic exhaustions for strictly convex domains.
Pluripotential theory, semigroups and boundary behavior of infinitesimal generators in strongly convex domains
Proper holomorphic mappings vs. peak points and Shilov boundary
We present a result on the existence of some kind of peak functions for ℂ-convex domains and for the symmetrized polydisc. Then we apply the latter result to show the equivariance of the set of peak points for A(D) under proper holomorphic mappings. Additionally, we present a description of the set of peak points in the class of bounded pseudoconvex Reinhardt domains.
Pseudodistances et courants positifs fermés dans les domaines de
Quantitative Bloch's theorem for certain classes of holomorphic mappings of the ball into Pn (C).
Quantitative estimates for the Green function and an application to the Bergman metric
Let be a bounded pseudoconvex domain that admits a Hölder continuous plurisubharmonic exhaustion function. Let its pluricomplex Green function be denoted by . In this article we give for a compact subset a quantitative upper bound for the supremum in terms of the boundary distance of and . This enables us to prove that, on a smooth bounded regular domain (in the sense of Diederich-Fornaess), the Bergman differential metric tends to infinity, for , when tends to a boundary point....
Remarks on the relative intrinsic pseudo-distance and hyperbolic imbeddability
We prove the invariance of hyperbolic imbeddability under holomorphic fiber bundles with compact hyperbolic fibers. Moreover, we show an example concerning the relation between the Kobayashi relative intrinsic pseudo-distance of a holomorphic fiber bundle and the one in its base.
Removable singularities for Bloch and normal functions
Schottky-Landau growth estimates for s-normal families of holomorphic mappings.
Schwarz-type lemmas for solutions of -inequalities and complete hyperbolicity of almost complex manifolds
The definition of the Kobayashi-Royden pseudo-metric for almost complex manifolds is similar to its definition for complex manifolds. We study the question of completeness of some domains for this metric. In particular, we study the completeness of the complement of submanifolds of co-dimension 1 or 2. The paper includes a discussion, with proofs, of basic facts in the theory of pseudo-holomorphic discs.
Some applications of the Bergman kernel to geometrical theory of functions
Some characterizations of Bloch functions on strongly pseudoconvex domains
Some remarks on a new pseudo-differential metric
Starrheitssätze für Produkte normierter Vektorräume endlicher Dimension und für Produkte hyperbolischer komplexer Räume.
Strange complex structures on Euclidean space.
Strengthened Moser’s conjecture, geometry of Grunsky coefficients and Fredholm eigenvalues
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = z: |z| > 1 can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible in a stronger sense, namely,...
Sur la caractérisation des automorphismes analytiques d'un domaine borné
Sur la caractérisation des isomorphismes analytiques entre domaines bornés d'un espace de Banach complexe