منابع مشابه
On completeness of the Bergman metric and its subordinate metric.
It is proved that on any bounded domain in the complex Euclidean space C(n) the Bergman metric is always greater than or equal to the Carathéodory distance. This leads to a number of interesting consequences. Here two such consequences are given. (i) The Bergman metric is complete whenever the Carathéodory distance is complete on a bounded domain. (ii) The Weil-Petersson metric is not uniformly...
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If D is a bounded open subset of C", the set H = {ƒ: D —> C| ƒ is holomorphic and SD\f\ 2 < +°°} is a separable infinite-dimensional Hubert space relative to the inner product <ƒ, g) = fDfg. The completeness of H can be seen from Cauchy integral estimates. Similar estimates show that for any p E D the functional ƒ H* ƒ(/?),ƒ£ H, is continuous. Thus there is a unique element KD(z, p) E f/ (as a ...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1983
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.80.10.3136