Proceedings of the American Mathematical Society

Author(s): Bo-Yong Chen
Journal: Proc. Amer. Math. Soc. 134 (2006), 139-148.
MSC (2000): Primary 32A25
Posted: August 15, 2005
Retrieve article in: PDF

Abstract: We prove a localization principle of the Bergman kernel form and metric for

pseudoconvex domains in the complex projective space. An estimate of the Bergman distance is also given.

1.: B. Berndtsson and Ph. Charpentier, A Sobolev mapping property of the Bergman kernel, Math. Z. 235 (2000), 1-10. MR 1785069 (2002a:32039)
2.: Z. Blocki, Estimates for the complex Monge-Ampère operator, Bull. Pol. Acad. Sci. 41 (1993), 151-157. MR 1414762 (97j:32009)
3.: -----, The Bergman metric and the pluricomplex Green function, MPI (Leipzig) preprint no: 85 (2002).
4.: Z. Blocki and P. Pflug, Hyperconvexity and Bergman completeness, Nagoya Math. J. 151 (1998), 221-225. MR 1650305 (2000b:32065)
5.: B. Y. Chen, Bergman completeness of hyperconvex manifolds, preprint.
6.: B. Y. Chen and J. H. Zhang, The Bergman metric on a Stein manifold with a bounded plurisubharmonic function, Trans. Amer. Math. Soc. 354 (2002), 2997-3009. MR 1897387 (2003c:32014)
7.: J. P. Demailly, Estimations pour l'opérateur d'un fibré vectoriel holomorphe semi-positiv au dessus d'une variété kählérienne complète Ann. Sci. Éc. Norm. Sup. 15 (1982), 457-511. MR 0690650 (85d:32057)
8.: -----, Mesures de Monge- $Amp\grave ere$ et mesures pluriharmoniques, Math. Z. 194 (1987), 519-564. MR 0881709 (88g:32034)
9.: K. Diederich, J. E. Fornaess and G. Herbort, Boundary behavior of the Bergman metric, Complex Analysis of Several Variables (Madison, Wis., 1982), 59-67, Proc. Sympos. Pure Math. 41, Amer. Math. Soc., Providence, RI, 1984. MR 0740872 (85j:32039)
10.: K. Diederich and T. Ohsawa, An estimate for the Bergman distance on pseudoconvex domains, Ann. of Math. 141 (1995), 181-190. MR 1314035 (95j:32039)
11.: -----, On pseudoconvex domains in $\mathbf{P}^n$ , Tokyo J. Math. 21 (1998), 353-358. MR 1663574 (99k:32024)
12.: R. E. Greene and H. Wu, Function theory on manifolds which possess a pole, Lecture Notes in Mathematics 699, Springer-Verlag, 1979. MR 0521983 (81a:53002)
13.: G. Herbort, The Bergman metric on hyperconvex domains, Math. Z. 232 (1999), 183-196. MR 1714284 (2000i:32020)
14.: M. Jarnicki and P. Pflug, Bergman completeness of complete circular domains, Ann. Pol. Math. Vol 50 (1989), 219-222. MR 1044868 (91f:32026)
15.: S. Kobayashi, Geometry of bounded domains, Trans. Amer. Math. Soc. 92 (1959), 267-290. MR 0112162 (22:3017)
16.: T. Ohsawa, Boundary behavior of the Bergman kernel function on pseudoconvex domains, Publ. RIMS, Kyoto Univ. 20 (1984), 897-902. MR 0764336 (86d:32025)
17.: -----, On the completeness of the Bergman metric, Proc. Jap. Acad. Sci. 57, Ser. A (1981), 238-240. MR 0618233 (82j:32053)
18.: T. Ohsawa and N. Sibony, Bounded p.s.h. functions and pseudoconvexity in Kähler manifolds, Nagoya Math. J. 149 (1998), 1-8. MR 1619572 (2000b:32062)
19.: T. Ohsawa and K. Takegoshi, On the extension of holomorphic functions, Math. Z. 195 (1987), 197-204. MR 0892051 (88g:32029)
20.: W. Zwonek, Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Dissert. Math. 388 (2000), 103 pp. MR 1785672 (2001h:32016)

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32A25

Bo-Yong Chen
Affiliation: Department of Applied Mathematics, Tongji University, Shanghai 200092, Peoples Republic of China
Address at time of publication: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464-8602, Japan
Email: by-chen@math.nagoya-u.ac.jp

DOI: 10.1090/S0002-9939-05-07780-4
PII: S 0002-9939(05)07780-4
Keywords: Bergman kernel form, Bergman metric, complex projective space
Received by editor(s): January 23, 2004
Posted: August 15, 2005
Additional Notes: This work was supported by JSPS
Communicated by: Mei-Chi Shaw
Copyright of article: Copyright 2005, American Mathematical Society

			Journals Home Search Author Info Subscribe Tech Support Help
ISSN 1088-6826 (e) ISSN 0002-9939 (p)

Previous issue \| Table of contents \| Next issue Articles in press \| Recently posted articles \| Most recent issue \| All issues Previous Article \| Next Article


	Comments: webmaster@ams.org © Copyright 2009, American Mathematical Society Privacy Statement		Search the AMS