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Displaying 61 – 80 of 92

Schwarz-type lemmas for solutions of $\bar{\partial}$ -inequalities and complete hyperbolicity of almost complex manifolds

Sergey Ivashkovich, Jean-Pierre Rosay (2004)

Annales de l'Institut Fourier

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.

Sharp bounds for the intersection of nodal lines with certain curves

Junehyuk Jung (2014)

Journal of the European Mathematical Society

Let $Y$ be a hyperbolic surface and let $φ$ be a Laplacian eigenfunction having eigenvalue $- 1 / 4 - τ^{2}$ with $τ > 0$ . Let $N (φ)$ be the set of nodal lines of $φ$ . For a fixed analytic curve $γ$ of finite length, we study the number of intersections between $N (φ)$ and $γ$ in terms of $τ$ . When $Y$ is compact and $γ$ a geodesic circle, or when $Y$ has finite volume and $γ$ is a closed horocycle, we prove that $γ$ is “good” in the sense of [TZ]. As a result, we obtain that the number of intersections between $N (φ)$ and $γ$ is $O (τ)$ . This bound is sharp.

Some characterizations of hyperbolic almost complex manifolds

Fathi Haggui, Adel Khalfallah (2010)

Annales Polonici Mathematici

First, we give some characterizations of the Kobayashi hyperbolicity of almost complex manifolds. Next, we show that a compact almost complex manifold is hyperbolic if and only if it has the Δ*-extension property. Finally, we investigate extension-convergence theorems for pseudoholomorphic maps with values in pseudoconvex domains.

Some remarks on a new pseudo-differential metric

Kyong T. Hahn (1981)

Annales Polonici Mathematici

Some remarks on the Casorati-Weierstrass theorem

Nessim Sibony, Pit-Mann Wong (1981)

Annales Polonici Mathematici

Starrheitssätze für Produkte normierter Vektorräume endlicher Dimension und für Produkte hyperbolischer komplexer Räume.

Konrad Peters (1974)

Mathematische Annalen

Strictly pseudohyperbolic domains.

Klas Diederich, John Erik Fornaess (1978)

Manuscripta mathematica

Sur les domaines hyperboliques pour la distance intégrée de Carathéodory

Jean-Pierre Vigué (1996)

Annales de l'institut Fourier

Dans cet article, je montre qu’un domaine $D$ est hyperbolique pour la pseudodistance intégrée de Carathéodory $c_{D}^{i}$ (c’est-à-dire que $c_{D}^{i}$ est une distance sur $D$ ) si et seulement si la pseudodistance de Carathéodory $c_{D}$ vérifie la propriété de séparation faible suivante : tout point $x$ de $D$ possède un voisinage $V$ tel que, pour tout point $y$ de $V$ , $y \neq x$ , $c_{D} (x, y)) \neq 0$ . Je construis aussi un exemple d’un domaine $c_{D}^{i}$ -hyperbolique et non $c_{D}$ -hyperbolique.

Tautness of locally taut domains in complex spaces

Do Duc Thai, Pham Nguyen Thu Trang (2004)

Annales Polonici Mathematici

A necessary and sufficient condition for tautness of locally taut domains in a weakly Brody hyperbolic complex space is given. Moreover, some results of Kobayashi and Gaussier are deduced as corollaries.

Teichmüller space is not Gromov hyperbolic.

Masur, Howard A., Wolf, Michael (1995)

Annales Academiae Scientiarum Fennicae. Series A I. Mathematica

The geometry of Teichmüller space via geodesic currents.

Francis Bonahon (1988)

Inventiones mathematicae

The Kobayashi-Pseudodistance on Homogeneous Manifolds.

Jörg Winkelmann (1990)

Manuscripta mathematica

The Serre Problem on Riemann Surfaces.

Ngaiming Mok (1981)

Mathematische Annalen

The three point pick problem on the bidisk.

Agler, Jim, McCarthy, John E. (2000)

The New York Journal of Mathematics [electronic only]

Three-dimensional hyperbolic geometry as ...-adic Arakelov geometry.

Yu I. Manin (1991)

Inventiones mathematicae

Un théorème de Bloch presque complexe

Benoît Saleur (2014)

Annales de l’institut Fourier

Cet article est consacré à la démonstration d’une version presque complexe du théorème de Bloch. Considérons la réunion C de quatre J-droites en position générale dans un plan projectif presque complexe. Nous démontrons que toute suite non normale de J-disques évitant évitant la configuration C admet une sous-suite convergeant, au sens de Hausdorff, vers une partie la réunion des diagonales de C. En particulier, le complémentaire de la configuration C est hyperboliquement plongé dans le paln projectif...

Un théorème de Green presque complexe

Julien Duval (2004)

Annales de l'Institut Fourier

On montre l'hyperbolicité du complémentaire de cinq droites en position générale dans un plan projectif presque complexe, répondant ainsi à une question de S. Ivashkovich.

Une remarque sur l'hyperbolicité injective

Jean-Pierre Vigué (1989)

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

In this Note, I prove that, in many cases, the injective Kobayashi pseudodistance, as defined by Hahn, is equal to the Kobayashi pseudodistance.

Uniformization of the leaves of a rational vector field

Alberto Candel, X. Gómez-Mont (1995)

Annales de l'institut Fourier

We study the analytic structure of the leaves of a holomorphic foliation by curves on a compact complex manifold. We show that if every leaf is a hyperbolic surface then they can be simultaneously uniformized in a continuous manner. In case the manifold is complex projective space a sufficient condition is that there are no algebraic leaf.

[unknown]

Lionel Darondeau (0)

Annales de l’institut Fourier

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