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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...

Berit Stensones (1989)

Mathematica Scandinavica

Proper holomorphic mappings in the special class of Reinhardt domains

Łukasz Kosiński (2007)

Annales Polonici Mathematici

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

Łukasz Kosiński, Włodzimierz Zwonek (2013)

Annales Polonici Mathematici

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.

Yifei Pan (1991)

Mathematische Zeitschrift

Proper holomorphic self-mappings of the minimal ball

Nabil Ourimi (2002)

Annales Polonici Mathematici

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 $V_{f}$ is factored by automorphisms if and only if $f_{*} (π ₁ (D ∖ f^{- 1} (f (V_{f})), x))$ is a normal subgroup of $π ₁ (Ω ∖ f (V_{f}), b)$ for some $b \in Ω ∖ f (V_{f})$ and $x \in f^{- 1} (b)$ .

Proper holomorphic self-mappings of the symmetrized bidisc

Armen Edigarian (2004)

Annales Polonici Mathematici

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

M. Landucci, S. Pinchuk (1995)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Proper Maps from Strongly q-Convex Domains.

Klas Diederich, John Eric Fornaess (1983)

Mathematische Annalen

Proper Self Maps of Weakly Pseudoconvex Domains.

Eric Bedford, Steve Bell (1982)

Mathematische Annalen

Pseudo holomorphic curves in symplectic manifolds.

M. Gromov (1985)

Inventiones mathematicae

Pull-back of currents by meromorphic maps

Tuyen Trung Truong (2013)

Bulletin de la Société Mathématique de France

Let $X$ and $Y$ be compact Kähler manifolds, and let $f : X \to Y$ be a dominant meromorphic map. Based upon a regularization theorem of Dinh and Sibony for DSH currents, we define a pullback operator $f^{♯}$ for currents of bidegrees $(p, p)$ of finite order on $Y$ (and thus foranycurrent, since $Y$ is compact). This operator has good properties as may be expected. Our definition and results are compatible to those of various previous works of Meo, Russakovskii and Shiffman, Alessandrini and Bassanelli, Dinh and Sibony, and can...

Punti fissi di mappe olomorfe

Bracci Filippo (2001)

Bollettino dell'Unione Matematica Italiana

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