Wandering subspaces and quasi-wandering subspaces in the Bergman space.
In this article we prove that every entire curve in a generic hypersurface of degree in is algebraically degenerated i.e there exists a proper subvariety which contains the entire curve.
A bounded open set with boundary of class C¹ which is locally weakly lineally convex is weakly lineally convex, but, as shown by Yuriĭ Zelinskiĭ, this is not true for unbounded domains. The purpose here is to construct explicit examples, Hartogs domains, showing this. Their boundary can have regularity or . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.
In this paper we introduce the notion of weak normal and quasinormal families of holomorphic curves from a domain in into projective spaces. We will prove some criteria for the weak normality and quasinormality of at most a certain order for such families of holomorphic curves.
We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.
We investigate the class of functions associated with the complex Hessian equation .
We show a very general existence theorem for a complex Monge-Ampère type equation on hyperconvex domains.
We prove several results on weak symplectic fillings of contact -manifolds, including: (1) Every weak filling of any planar contact manifold can be deformed to a blow up of a Stein filling. (2) Contact manifolds that have fully separating planar torsion are not weakly fillable—this gives many new examples of contact manifolds without Giroux torsion that have no weak fillings. (3) Weak fillability is preserved under splicing of contact manifolds along symplectic pre-Lagrangian tori—this gives many...
The main result of this paper is the following: if the Weierstrass division theorem is valid in a quasianalytic differentiable system, then this system is contained in the system of analytic germs. This result has already been known for particular examples, such as the quasianalytic Denjoy-Carleman classes.