Picard-Borel-Eigenschaft und Anwendungen.
Pluri-canonical divisors on Kähler manifolds.
Precise regularity up to the boundary of proper holomorphic mappings
Proper holomorphic liftings and new formulas for the Bergman and Szegő kernels
We consider a large class of convex circular domains in which contains the oval domains and minimal balls. We compute their Bergman and Szegő kernels. Our approach relies on the analysis of some proper holomorphic liftings of our domains to some suitable manifolds.
Proper holomorphic mappings.
Proper holomorphic mappings between bounded complete Reinhardt domains in C2.
Proper Holomorphic Mappings Between Real-Analytic Pseudoconvex Domains in Cn.
Proper holomorphic mappings between Reinhards domains and pseudoellipsoids
Proper holomorphic mappings between rigid polynomial domains in Cn+1.
We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in Cn+1. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic self-mappings between such domains are biholomorphic.
Proper holomorphic mappings from strongly pseudoconvex domains in C... to the unit polydisc in C...
Proper holomorphic mappings in the special class of Reinhardt domains
A complete characterization of proper holomorphic mappings between domains from the class of all pseudoconvex Reinhardt domains in ℂ² with the logarithmic image equal to a strip or a half-plane is given.
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.
Proper holomorphic self-mappings of Reinhardt domains.
Proper holomorphic self-mappings of the minimal ball
The purpose of this paper is to prove that proper holomorphic self-mappings of the minimal ball are biholomorphic. The proof uses the scaling technique applied at a singular point and relies on the fact that a proper holomorphic mapping f: D → Ω with branch locus is factored by automorphisms if and only if is a normal subgroup of for some and .
Proper holomorphic self-mappings of the symmetrized bidisc
We characterize proper holomorphic self-mappings 𝔾₂ → 𝔾₂ for the symmetrized bidisc 𝔾₂ = {(λ₁+λ₂,λ₁λ₂): |λ₁|,|λ₂| < 1} ⊂ ℂ².
Proper mappings between Reinhardt domains with an analytic variety on the boundary