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Weak lineal convexity

Christer O. Kiselman (2015)

Banach Center Publications

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 C 1 , 1 or C . Obstructions to constructing smoothly bounded domains with certain homogeneity properties will be discussed.

Weak normal and quasinormal families of holomorphic curves

Si Duc Quang, Dau Hong Quan (2018)

Archivum Mathematicum

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.

Weak symplectic fillings and holomorphic curves

Klaus Niederkrüger, Chris Wendl (2011)

Annales scientifiques de l'École Normale Supérieure

We prove several results on weak symplectic fillings of contact 3 -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...

Weierstrass division theorem in quasianalytic local rings

Abdelhafed Elkhadiri, Hassan Sfouli (2008)

Studia Mathematica

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.

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