Article contents
Bergman completeness of hyperconvex manifolds
Published online by Cambridge University Press: 22 January 2016
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
We proved that any hyperconvex manifold has a complete Bergman metric.
Keywords
- Type
- Research Article
- Information
- Copyright
- Copyright © Editorial Board of Nagoya Mathematical Journal 2004
References
[1]
Blocki, Z., Estimates for the complex Monge-Ampere operator, Bull. Pol. Acad. Sci., 41 (1993), 151–157.Google Scholar
[2]
Blocki, Z. and Pflug, P., Hyperconvexity and Bergman completeness, Nagoya Math. J., 151 (1998), 221–225.CrossRefGoogle Scholar
[3]
Chen, B. Y., Completeness of the Bergman metric on non-smooth pseudoconvex domains, Ann. Pol. Math., LXXI (1999), 241–251.CrossRefGoogle Scholar
[4]
Chen, B. Y. and Zhang, J. H., The Bergman metric on a Stein manifold with a bounded plurisubharmonic function, Trans. Amer. Math. Soc., 354 (2002), 2997–3009.CrossRefGoogle Scholar
[5]
Demailly, J. P., Estimations L2 pour l’opérateur d’un fibré vectoriel holomorphe semi-positiv au dessus d’une variété kählérienne complète, Ann. Sci. Ec. Norm. Sup., 15 (1982), 457–511.CrossRefGoogle Scholar
[6]
Demailly, J. P., Mesures de Monge-Ampère et mesures pluriharmoniques, Math. Z., 194 (1987), 519–564.CrossRefGoogle Scholar
[7]
Greene, R. E. and Wu, H., Function theory on manifolds which possess a pole, Lecture Notes in Mathematics, 699, Springer-Verlag
1979.CrossRefGoogle Scholar
[8]
Herbort, G., The Bergman metric on hyperconvex domains, Math. Z., 232 (1999), 183–196.CrossRefGoogle Scholar
[9]
Jarnicki, M. and Pflug, P., Bergman completeness of complete circular domains, Ann. Pol. Math., 50 (1989), 219–222.CrossRefGoogle Scholar
[10]
Kobayashi, S., Geometry of bounded domains, Trans. Amer. Math. Soc. 92 (1959), 267–290.CrossRefGoogle Scholar
[11]
Kobayashi, S., Hyperbolic Complex spaces, A Series of Comprehensive Studies in Mathematics, 318, Springer-Verlag
1998.Google Scholar
[12]
Ohsawa, T., Boundary behavior of the Bergman kernel function on pseudoconvex domains, Publ. RIMS, Kyoto Univ., 20 (1984), 897–902.CrossRefGoogle Scholar
[13]
Ohsawa, T. and Sibony, N., Bounded p.s.h. functions and pseudoconvexity in Kähler manifolds, Nagoya Math. J., 149 (1998), 1–8.CrossRefGoogle Scholar
[14]
Richberg, R., Steige streng pseudoconvexe Funktionen, Math. Ann., 175 (1968), 257–286.Google Scholar
You have
Access
- 15
- Cited by