It is shown that the unit ball in ${{\mathbb{C}}^{n}}$ is the only complexmanifold that can universally cover both Stein and non-Stein strictly pseudoconvex domains.

Suppose $G$ is a connected complex Lie group and $H$ is a closed complex subgroup. Then there exists a closed complex subgroup $J$ of $G$ containing $H$ such that the fibration $\pi :G/H\to $$G/J$ is the holomorphic reduction of $G/H$i.e., $G/J$ is holomorphically separable and $\mathcal{O}(G/H)\cong $${{\pi }^{*}}\mathcal{O}(G/J)$. In this paper we prove that if $G/H$ is pseudoconvex, i.e., if $G/H$ admits a continuous plurisubharmonic exhaustion function, then $G/J$ is Stein and $J/H$ has no non-constant holomorphic functions.

We give a method for constructing a Legendrian representative of a knot in $S^{3}$ which realizes its maximal Thurston–Bennequin number under a certain condition. The method utilizes Stein handle decompositions of $D^{4}$ , and the resulting Legendrian representative is often very complicated (relative to the complexity of the topological knot type). As an application, we construct infinitely many knots in $S^{3}$ each of which yields a reducible 3-manifold by a Legendrian surgery in the standard tight contact structure. This disproves a conjecture of Lidman and Sivek.

In this paper we study the classification of holomorphic flows on Stein spaces of dimension two. We assume that the flow has periodic orbits, not necessarily with a same period. Then we prove a linearization result for the flow, under some natural conditions on the surface.