Completeness of the Bergman metric on non-smooth pseudoconvex domains
نویسندگان
چکیده
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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where (h) is the inverse of the matrix (hij), ∆M = ∑ i,j h ∂ij and Γ s tγ denote the Christoffel symbols of the Hermitian metric g on N . It follows from (1.1) that if u is holomorphic, then u must be harmonic. Thus, it is natural to ask under what circumstances a harmonic map is holomorphic or antiholomorphic. Under the assumption that both M and N are compact, Siu [31] demonstrated that if th...
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ژورنال
عنوان ژورنال: Annales Polonici Mathematici
سال: 1999
ISSN: 0066-2216,1730-6272
DOI: 10.4064/ap-71-3-241-251