A characterization of the ball
We study bounded domains with certain smoothness conditions and the properties of their squeezing functions in order to prove that the domains are biholomorphic to the ball.
math.CV↗
arXiv subjects
Klas Diederich
Publications and source records attributed to Klas Diederich.
Boundary Behavior of the Bergman Metric
More precise estimates for the Bergman metric on strongly pseudoconvex domains are given, based on the use of the squeezing function.
math.CV↗
Exposing points on the boundary of a strictly pseudoconvex or a locally convexifiable domain of finite 1-type
We show that for any bounded domain $Ω\subset\Cp ^n$ of 1-type $2k $ which is locally convexifiable at $p\in bΩ$, having a Stein neighborhood basis, there is a biholomorphic map $f:\barΩ\rightarrow \Cp ^n $ such that $f(p)$ is a global extreme point of type $2k$ for $f{(\barΩ)}$.
math.CV↗
Diffeomorphisms of Stein structures
We prove that a pseudoholomorphic diffeomorphism between two almost complex manifolds with boundaries satisfying some pseudoconvexity type condition cannot map a pseudoholomorphic disc in the boundary to a single point. This can be viewed as an almost complex analogue of a well-known theorem of J. E. Fornaess.
math.CV↗
Plurisubharmonic exhaustion functions and almost complex Stein structures
We prove that a relatively compact pseudoconvex domain with smooth boundary in an almost complex manifold admits a bounded strictly plurisubharmonic exhaustion function. We use this result for the study of convexity and hyperbolicity properties of these domains and the contact geometry of their boundaries.
math.CV↗