Proceedings of the National Academy of Sciences · 1976 · 32 citations · 2 references
Natural SciencesAstronomyAnalytic PhilosophyLandscape MetricsTopologyComplex GeometryMetric GeometryMetric SpacesBergman SpacesCompactness TheoremsComplete Metric SpacesCompletion Of Metric SpacesRiemann SurfacesTeichmüller Theory
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 equivalent to the Bergman metric in the Teichmüller space T(g) of any Riemann surface of genus g >/= 2.
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