Title: About the Caratheodory Completeness of all Reinhardt Domains
Abstract: In the theory of complex analysis, there are different notions of distances on a bounded domain, for example, the Caratheodory-distance dealing with bounded holomorphic functions, the Bergmann-metric measuring how many L2-holomorphic functions exist, or the Kobayashi-distance, describing the sizes of analytic discs in G. The main problem working with these distances is to decide the domain G that is complete with respect to one of the distances. Any pseudo-convex domain with C1-boundary is complete with respect to the Bergmann-metric. The Caratheodory-distance can be compared with the other two, in fact, it is the smallest one, but there is no relation between the Bergmann-metric and the Kobayashi-metric. Any bounded complete Reinhardt domain G that is pseudo-convex is complete in the sense of the Caratheodory-distance; in fact, it is proved that any Caratheodory ball is a relatively compact subset of G.
Publication Year: 1984
Publication Date: 1984-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
Access and Citation
Cited By Count: 12
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot