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Displaying 81 – 100 of 218

Extension of holomorphic maps between real hypersurfaces of different dimension

Rasul Shafikov, Kausha Verma (2007)

Annales de l’institut Fourier

In this paper we extend the results on analytic continuation of germs of holomorphic mappings from a real analytic hypersurface to a real algebraic hypersurface to the case when the target hypersurface is of higher dimension than the source. More precisely, we prove the following: Let $M$ be a connected smooth real analytic minimal hypersurface in $C^{n}$ , $M^{'}$ be a compact strictly pseudoconvex real algebraic hypersurface in $C^{N}$ , $1 < n \leq N$ . Suppose that $f$ is a germ of a holomorphic map at a point $p$ in $M$ and $f (M)$ is in...

Extension of Holomorphic Maps into Hermitian Manifolds.

Bernhard SHIFFMAN (1971)

Mathematische Annalen

Extension of line bundles and holomorphic maps

S. M. Ivashkovich (1988)

Matematički Vesnik

Extension of Positive Line Bundles and Meromorphic Maps.

Bernard Shiffman (1971/1972)

Inventiones mathematicae

Extension of Proper Holomorphic Mappings Past the Boundary.

Eric Bedford, Steve Bell (1985)

Manuscripta mathematica

Extension of separately holomorphic functions defined in non-open sets in the infinite dimensional case

Ludwik M. Drużkowski (1983)

Annales Polonici Mathematici

Extension of separately holomorphic functions-a survey 1899-2001

Peter Pflug (2003)

Annales Polonici Mathematici

This note is an attempt to describe a part of the historical development of the research on separately holomorphic functions.

Extension theorems of Sakai type for separately holomorphic and meromorphic functions

Peter Pflug, Viêt Anh Nguyên (2003)

Annales Polonici Mathematici

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

Extensions of Rings of Holomorphic Functions.

E.L. Stout (1972)

Mathematische Annalen

Families of analytic discs in $𝐂^{n}$ with boundaries on a prescribed $C R$ submanifold

C. Denson Hill, Geraldine Taiani (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Fortsetzbarkeit k-analytischer Mengen.

Werner Lütkebohmert (1975)

Mathematische Annalen

Fortsetzbarkeit k-meromorpher Funktionen.

Werner Lütkebohmert (1976)

Mathematische Annalen

Fourier and Poisson transformation associated to a semisimple Symmetrie space.

G. Olafsson (1987)

Inventiones mathematicae

Geometry of hypersurfaces and mapping theorems in Cn.

D., Jr. Burns, S. Shnider (1979)

Commentarii mathematici Helvetici

Germs of holomorphic mappings between real algebraic hypersurfaces

Nordine Mir (1998)

Annales de l'institut Fourier

We study germs of holomorphic mappings between general algebraic hypersurfaces. Our main result is the following. If $(M, p_{0})$ and $(M^{'}, p_{0}^{'})$ are two germs of real algebraic hypersurfaces in $ℂ^{N + 1}$ , $N \geq 1$ , $M$ is not Levi-flat and $H$ is a germ at $p_{0}$ of a holomorphic mapping such that $H (M) \subseteq M^{'}$ and $Jac (H) ≢ 0$ then the so-called reflection function associated to $H$ is always holomorphic algebraic. As a consequence, we obtain that if $M^{'}$ is given in the so-called normal form, the transversal component of $H$ is always algebraic. Another corollary of...

Graphs with multiple sheeted pluripolar hulls

Evgeny Poletsky, Jan Wiegerinck (2006)

Annales Polonici Mathematici

We study the pluripolar hulls of analytic sets. In particular, we show that hulls of graphs of analytic functions can be multiple sheeted and sheets can be separated by a set of zero dimension.

Hartogs extension phenomena for analytic curves.

Yeren Xu (1994)

Mathematische Zeitschrift

Hartogs type extension theorems on some domains in Kähler manifolds

Takeo Ohsawa (2012)

Annales Polonici Mathematici

Given a locally pseudoconvex bounded domain Ω, in a complex manifold M, the Hartogs type extension theorem is said to hold on Ω if there exists an arbitrarily large compact subset K of Ω such that every holomorphic function on Ω-K is extendible to a holomorphic function on Ω. It will be reported, based on still unpublished papers of the author, that the Hartogs type extension theorem holds in the following two cases: 1) M is Kähler and ∂Ω is C²-smooth and not Levi flat; 2) M is compact Kähler and...

Holomorphe Korrespondenzen und meromorphe Abbildungen allgemeiner komplexer Räume.

Günther Kraus (1972)

Manuscripta mathematica

Holomorphic and Meromorphic Mappings and Curvature.

Bernard Shiffman (1976)

Mathematische Annalen

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