期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：1976
卷号：73
期号：12
页码：4294-4294
DOI：10.1073/pnas.73.12.4294
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：It is proved that on any bounded domain in the complex Euclidean space Cn the Bergman metric is always greater than or equal to the Caratheodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Caratheodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly equivalent to the Bergman metric in the Teichmuller space T(g) of any Riemann surface of genus g [≥] 2.
关键词：Carathéodory differential metric ; Weil-Petersson metric ; Teichmüller space
