Balls defined by nonsmooth vector fields and the Poincaré inequality
We provide a structure theorem for Carnot-Carathéodory balls defined by a family of Lipschitz continuous vector fields. From this result a proof of Poincaré inequality follows.
Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in with real analytic boundary
It is shown that given a bounded strictly convex domain in with real analitic boundary and a point in , there exists a larger bounded strictly convex domain with real analitic boundary, close as wished to , such that is a ball for the Kobayashi distance of with center . The result is applied to prove that if is not biholomorphic to the ball then any automorphism of extends to an automorphism of .
Behavior of invariant metrics near convexifiable boundary points
The behaviour of the Carathéodory, Kobayashi and Azukawa metrics near convex boundary points of domains in is studied.
Behavior of the Carathéodory metric near strictly convex boundary points.
Bemerkungen zur Deformationstheorie nichtrationaler Singularitäten.
Bergman completeness of Zalcman type domains
We give an equivalent condition for Bergman completeness of Zalcman type domains. This also solves a problem stated by Pflug.
Bergman-Shilov boundary for subfamilies of q-plurisubharmonic functions
We introduce the notion of the Shilov boundary for some subfamilies of upper semicontinuous functions on a compact Hausdorff space. It is by definition the smallest closed subset of the given space on which all functions of that subclass attain their maximum. For certain subfamilies with simple structure we show the existence and uniqueness of the Shilov boundary. We provide its relation to the set of peak points and establish Bishop-type theorems. As an application we obtain a generalization of...
Beschränkte Integraloperatoren auf streng q-konvexen Gebieten in Cn.
Beschränkte Lösungen der Cauchy-Riemannschen Differentialgleichungen auf q-konkaven Gebieten.
Big Picard theorems for holomorphic mappings into the complement of moving hypersurfaces in .
Boundary behaviour of invariant distances and complex geodesics
In questa Nota viene studiato il comportamento al bordo delle distanze di Carathéodory e Kobayashi in domini fortemente pseudoconvessi di classe . Come applicazione si dimostra che ogni geodetica complessa in tali domini è estendibile al bordo di classe .