In this short paper, we show that the only proper holomorphic self-maps of bounded domains in ${ℂ}^k$ whose iterates approach a strictly pseudoconvex point of the boundary are automorphisms of the euclidean ball. This is a Wong-Rosay type theorem for a sequence of maps whose degrees are a priori unbounded.

Soit $G_{\mathbf{C}}$ un groupe de Lie complexe et $G_{\mathbf{R}}$ une forme réelle fermée de $G_{\mathbf{C}}$. Un couple $(G_{\mathbf{C}},G_{\mathbf{R}})$ est dit pseudo-convexe, s’il existe sur $G_{\mathbf{C}}$ une fonction régulière, strictement p.s.h., invariante par l’action de $G_{\mathbf{R}}$ et d’exhaustion sur $G_{\mathbf{C}}/G_{\mathbf{R}}$. On dit que $G_{\mathbf{R}}$ est à spectre imaginaire pur, si pour tout $X$ de Lie$\left(G_{\mathbf{R}}\right)$, les valeurs propres de ad$X$ sont imaginaires pures. Pour $G_{\mathbf{C}}$ à radical simplement connexe, cette dernière propriété équivaut à la pseudo-convexité de $(G_{\mathbf{C}},G_{\mathbf{R}})$. Pour $(G_{\mathbf{C}},G_{\mathbf{R}})$ pseudo-convexe et sous une hypothèse de sous-groupe discret,...

We prove that every compact, normal Riemannian homogeneous manifold admits an adapted complex structure on its entire tangent bundle.

This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem...

The aim of this note is to give a clearer and more direct proof of the main result of another paper of the author. Moreover, we give some complementary results related to R-complete algebraic foliations with R a rational function of type ℂ*.

Let $G$ be a connected complex Lie group, $H$ a closed, complex subgroup of $G$ and $X:=G/H$. Let $R$ be the radical and $S$ a maximal semisimple subgroup of $G$. Attempts to construct examples of noncompact manifolds $X$ homogeneous under a nontrivial semidirect product $G=S⋉R$ with a not necessarily $G$-invariant Kähler metric motivated this paper. The $S$-orbit $S/S\cap H$ in $X$ is Kähler. Thus $S\cap H$ is an algebraic subgroup of $S$ [4]. The Kähler assumption on $X$ ought to imply the $S$-action on the base $Y$ of any homogeneous fibration $X\to Y$ is algebraic...

Using exhaustion properties of invariant plurisubharmonic functions along with basic combinatorial information on toric varieties, we prove convergence results for sequences of densities $|{\varphi }_n{|}^2=|s_N{|}^2/\left|\right|s_N{\left|\right|}_{L^2}^2$ for eigensections $s_N\in \Gamma (X,L^N)$ approaching a semiclassical ray. Here $X$ is a normal compact toric variety and $L$ is an ample line bundle equipped with an arbitrary positive bundle metric which is invariant with respect to the compact form of the torus. Our work was motivated by and extends that of Shiffman, Tate and Zelditch....

We show that proper holomorphic self maps of pseudoconvex rigid polynomial domains in C2 are automorphisms.

We show that the local automorphism group of a minimal real-analytic CR manifold $M$ is a finite dimensional Lie group if (and only if) $M$ is holomorphically nondegenerate by constructing a jet parametrization.

In questa Nota viene dato un nuovo metodo elementare per determinare il gruppo degli automorfismi del primo dominio classico. In una Nota successiva, con procedimenti del tutto analoghi verranno determinati i gruppi degli automorfismi del terzo e del quarto dominio classico.