We establish a lower estimate for the Kobayashi-Royden infinitesimal pseudometric on an almost complex manifold $(M,J)$ admitting a bounded strictly plurisubharmonic function. We apply this result to study the boundary behaviour of the metric on a strictly pseudoconvex domain in $M$ and to give a sufficient condition for the complete hyperbolicity of a domain in $(M,J)$.

Suppose that $Y$ is a complex manifold such that any holomorphic map from a compact convex set in a Euclidean space ${ℂ}^n$ to $Y$ is a uniform limit of entire maps ${ℂ}^n\to Y$. We prove that a holomorphic map $X_0\to Y$ from a closed complex subvariety $X_0$ in a Stein manifold $X$ admits a holomorphic extension $X\to Y$ provided that it admits a continuous extension. We then establish the equivalence of four Oka-type properties of a complex manifold.

The purpose of this article is twofold. The first is to show a criterion for the normality of holomorphic mappings into Abelian varieties; an extension theorem for such mappings is also given. The second is to study the convergence of meromorphic mappings into complex projective varieties. We introduce the concept of d-convergence and give a criterion of d-normality of families of meromorphic mappings.

Let f : M → M' be a CR homeomorphism between two minimal, rigid polynomial varieties of Cn without holomorphic curves. We show that f extends biholomorphically in a neighborhood of M if f extends holomorphically in a neighborghood of a point p0 ∈ M or if f is of class C1. In the other hand, in case M and M' are two algebraic hypersurfaces, we obtain the extension without supplementary conditions.

We study the extension problem for germs of holomorphic isometries $f:(D;x_0)\to (\Omega ;f\left(x_0\right))$ up to normalizing constants between bounded domains in Euclidean spaces equipped with Bergman metrics $d{s}_D^2$ on $D$ and $d{s}_{\Omega }^2$ on $\Omega$. Our main focus is on boundary extension for pairs of bounded domains $(D,\Omega )$ such that the Bergman kernel $K_D(z,w)$ extends meromorphically in $(z,\overline{w})$ to a neighborhood of $\overline{D}\times D$, and such that the analogous statement holds true for the Bergman kernel $K_{\Omega }(\varsigma ,\xi )$ on $\Omega$. Assuming that $(D;d{s}_D^2)$ and $(\Omega ;d{s}_{\Omega }^2)$ are complete Kähler manifolds, we prove that the germ...

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 $C^n$, $M^{\prime }$ be a compact strictly pseudoconvex real algebraic hypersurface in $C^N$, $1\<n\le N$. Suppose that $f$ is a germ of a holomorphic map at a point $p$ in $M$ and $f\left(M\right)$ is in...

This paper deals with the finiteness problem of meromorphic funtions on an annulus sharing four values regardless of multiplicity. We prove that if three admissible meromorphic functions $f_1$, $f_2$, $f_3$ on an annulus $𝔸\left(R_0\right)$ share four distinct values regardless of multiplicity and have the complete identity set of positive counting function, then $f_1=f_2$ or $f_2=f_3$ or $f_3=f_1$. This result deduces that there are at most two admissible meromorphic functions on an annulus sharing a value with multiplicity truncated to level $2$ and...

We prove some finiteness theorems for differential nondegenerate meromorphic mappings of ${ℂ}^m$ into ℙⁿ(ℂ) which share n+3 hyperplanes.

Soit $\pi :V\to W$ un morphisme propre fini et surjectif entre deux variétés analytiques complexes. Nous donnons une caractérisation des fonctions (continues) sur $W$ qui sont de la forme ${\pi }_{*}f$ où $f$ est une fonction $C^{\infty }$ sur $V$. Pour cela nous introduisons la notion de fonction de type trace sur une variété analytique complexe. Ces fonctions sont analytiques réelles en dehors d’une hypersurface complexe et admettent des singularités très simples aux points de cette hypersurface.