Principal Orbit Types for Reductive Groups Acting on Stein Manifolds.
Soit un ouvert relativement compact et localement pseudo-convexe de la variété analytique .Alors,1) Si le fibré tangent est positif, est -convexe.2) Si admet une fonction strictement plurisousharmonique, est de Stein.3) Si est l’espace total d’un morphisme de Stein à base de Stein, est de Stein.
The general Stein union problem is solved: given an increasing sequence of Stein open sets, it is shown that the union is Stein if and only if is Hausdorff separated.
A necessary and sufficient condition, which is a weak converse of a classical theorem of Behnke-Stein, in order that a limit of Stein spaces be again a Stein space is proved.