Proper Holomorphic Self-maps Research Articles

Proper Holomorphic self-maps of quasi-circular domains in C2

In this paper, we prove that every proper holomorphic self-map of a smoothly bounded pseudoconvex circular or Hartogs domain of finite type in C2 is biholomorphic.

Proper holomorphic mappings between rigid polynomial domains in $\mathbb{C}^{n+1}$

We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in $\mathbb{C}^{n+1}$. 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.

On proper holomorphic mappings from domains with T-action

AbstractWe describe the branch locus of a proper holomorphic mapping between two smoothly bounded pseudoconvex domains of finite type in under the assumption that the first domain admits a transversal holomorphic action of the unit circle. As an application we show that any proper holomorphic self-mapping of a smoothly bounded pseudoconvex complete circular domain of finite type in is biholomorphic.

Holomorphic vector fields and proper holomorphic self-maps of Reinhardt domains

Holomorphic vector fields and proper holomorphic self-maps of Reinhardt domains

Spherical hypersurfaces and lattes rational maps

Any rational map f is induced on the Riemann sphere by a homogeneous non-degenerate polynomial map F on C 2. By the work of J. E. Fornaess and N. Sibony or J. Hubbard and P. Papadopol, one knows that bΩ F , the boundary of the basin of attraction of F at the origin, is Levi-flat above the Fatou set of f. Nothing is known about bΩ F when the Fatou set of f is empty. In this direction, we characterize the Lattès rational maps by a geometrical property of bΩ F . It turns out that these basins, which we explicitely describe, are the first examples of essentially strictly pseudoconvex domains which do admit non-injective proper holomorphic self-maps.

On proper holomorphic self-maps of generalized complex ellipsoids

The purpose of this paper is to prove that every proper holomorphic self-mapping of a Reinhardt domain Ω in C n which is a generalization of a complex ellipsoid is biholomorphic. The main novelty of our result is that Ω is a domain in C n such that it is allowed to have a boundary point at which the Levi determinant has infinite order of vanishing.

Proper holomorphic self-mappings of hartogs domains in

In this paper it is proved that every paper holomorphic self mapping of a certain Hartogs domain is biholomorphic.

Proper holomorphic self-mappings of Hartogs domains in ${\bf C}^2$.

Proper holomorphic self-mappings of Hartogs domains in ${\bf C}^2$.

Proper holomorphic self-maps of plane regions

If ω is a connected open set in C, whose connectivity is finite hut larger than 2, then every proper holomorphic map from R to Cl is one-to-one. On the orher hand , for every positive integer m there are regions ω ⊂C, of infinite connectiviry, which admit proper holomorphic self-maps of mulitiplicity m. ∗

Holomorphic mappings from the ball and polydisc

Introduction. The holomorphic self-homeomorphisms (automorphisms) of the open unit ball B, in ~L TM have long been known [1] - they are given by certain rational functions which are holomorphic on a neighborhood of Bn and induce a homeomorphism of the boundary, bB,, of the ball. Our first result can be viewed as a local characterization of these automorphisms: For n > 1, a nonconstant holomorphic mapping into ~ which is defined in a neighborhood of a point of bB, and which maps bB, into itself is necessarily an automorphism, or, more precisely, extends to be an automorphism. We apply this to obtain some information on the as yet unsettled question as to whether every proper holomorphic self-mapping of Bn is an automorphism. In particular, we recover (Cor. 1.1) a result of Pelles ([3, 5]). In the second part, we consider holomorphic mappings from polydiscs. According to a classical theorem of Poincar6, there exists no biholomorphism from the polydisc U z in C 2 with the ball B2. We obtain some integral formulas which yield a quantitative explanation of this phenomenon, Finally I wish to acknowledge that the above characterization of automorphisms may have been known to the late Professor L6wner, at least for two complex variables. I want to thank Professors L. Bers and C. Titus for this information on their oral communication with L6wner.

Correction to my paper: Proper holomorphic self-maps of the unit ball

Correction to my paper: Proper holomorphic self-maps of the unit ball

Proper holomorphic self-maps of the unit ball

Proper holomorphic self-maps of the unit ball