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Sur l'intersection des courants laminaires.

Romain Dujardin (2004)

Publicacions Matemàtiques

We try to find a geometric interpretation of the wedge product of positive closed laminar currents in C2. We say such a wedge product is geometric if it is given by intersecting the disks filling up the currents. Uniformly laminar currents do always intersect geometrically in this sense. We also introduce a class of strongly approximable laminar currents, natural from the dynamical point of view, and prove that such currents intersect geometrically provided they have continuous potentials.

Survey of Oka theory.

Forstnerič, Franc, Lárusson, Finnur (2011)

The New York Journal of Mathematics [electronic only]

The automorphism groups of Zariski open affine subsets of the affine plane

Zbigniew Jelonek (1994)

Annales Polonici Mathematici

We study some properties of the affine plane. First we describe the set of fixed points of a polynomial automorphism of ℂ². Next we classify completely so-called identity sets for polynomial automorphisms of ℂ². Finally, we show that a sufficiently general Zariski open affine subset of the affine plane has a finite group of automorphisms.

The Bergman kernel of the minimal ball and applications

Karl Oeljeklaus, Peter Pflug, El Hassan Youssfi (1997)

Annales de l'institut Fourier

In this note we compute the Bergman kernel of the unit ball with respect to the smallest norm in ℂ n that extends the euclidean norm in ℝ n and give some applications.

The dynamics of holomorphic maps near curves of fixed points

Filippo Bracci (2003)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let M be a two-dimensional complex manifold and f : M → M a holomorphic map. Let S ⊂ M be a curve made of fixed points of f , i.e.  Fix ( f ) = S . We study the dynamics near  S in case  f acts as the identity on the normal bundle of the regular part of  S . Besides results of local nature, we prove that if  S is a globally and locally irreducible compact curve such that S · S < 0 then there exists a point p ∈ S and a holomorphic f -invariant curve with  p on the boundary which is attracted by  p under the action of  f . These results are achieved...

The ends of discs

Josip Globevnik, Edgar Lee Stout (1986)

Bulletin de la Société Mathématique de France

The existence of angular derivatives of holomorphic maps of Siegel domains in a generalization of C * -algebras

Kazimierz Włodarczyk (1994)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The aim of this paper is to start a systematic investigation of the existence of angular limits and angular derivatives of holomorphic maps of infinite dimensional Siegel domains in J * -algebras. Since J * -algebras are natural generalizations of C * -algebras, B * -algebras, J ⁢ C * -algebras, ternary algebras and complex Hilbert spaces, various significant results follow. Examples are given.

The fixed points of holomorphic maps on a convex domain

Do Duc Thai (1992)

Annales Polonici Mathematici

We give a simple proof of the result that if D is a (not necessarily bounded) hyperbolic convex domain in ℂ n then the set V of fixed points of a holomorphic map f:D → D is a connected complex submanifold of D; if V is not empty, V is a holomorphic retract of D. Moreover, we extend these results to the case of convex domains in a locally convex Hausdorff vector space.

The Fujiki class and positive degree maps

Gautam Bharali, Indranil Biswas, Mahan Mj (2015)

Complex Manifolds

We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.

The growth of regular functions on algebraic sets

A. Strzeboński (1991)

Annales Polonici Mathematici

We are concerned with the set of all growth exponents of regular functions on an algebraic subset V of ℂ n . We show that its elements form an increasing sequence of rational numbers and we study the dependence of its structure on the geometric properties of V.

Currently displaying 381 – 400 of 463