As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in stud...As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in studying the boundary geometry of the domain and biholo-morphic mappings extending smoothly to the boundaries of the relevant domains.展开更多
S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to...S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. Complete Einstein-Kahler metric with Explicit form, however, is only known in the case of homogeneous domain.展开更多
基金Supported by NSFC(No.10171068,No.10071051),NSF of Beijing(No.1012004)and Planned Project for the Development of Science and Technology,Beijing Eduction Committee.
文摘As is known to all, theory of invariant metric is very important inseveral complex analysis.The Bergman, Caratheodory and Kobayashi metrics are important biholomorphic. invariants.They play very important role in studying the boundary geometry of the domain and biholo-morphic mappings extending smoothly to the boundaries of the relevant domains.
基金Supported in part by NSFC(Grant No.:10171068,10171051)and NSF of Bejing(Grant No. 1012004).
文摘S. Y. Cheng and S. T. Yau showed in [CY] that any C2 bounded pseudoconvex domain in C?has a complete Einstein-Kahler metric with constant negative Ricci curvature. N. Mok and S. T. Yau[MY] have extended this result to arbitrary bounded pseudoconvex domain in Cn. Complete Einstein-Kahler metric with Explicit form, however, is only known in the case of homogeneous domain.
