Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A remark on the Bergman stability


Authors: Chen Boyong and Zhang Jinhao
Journal: Proc. Amer. Math. Soc. 128 (2000), 2903-2905
MSC (1991): Primary 32H10
DOI: https://doi.org/10.1090/S0002-9939-00-05333-8
Published electronically: February 29, 2000
MathSciNet review: 1664329
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract:

Let $\{D_k\},k=1,2,\cdots$, be a sequence of bounded pseudoconvex domains that converges, in the sense of Boas, to a bounded domain $D$. We show that if $\partial D $ can be described locally as the graph of a continuous function in suitable coordinates for ${\mathbf C}^n$, then the Bergman kernel of $D_k$ converges to the Bergman kernel of $D$ uniformly on compact subsets of $D\times D$.


References [Enhancements On Off] (What's this?)

  • 1. H.P. Boas, The Lu Qi-Keng conjecture fails generically, Proc. Amer. Soc. 124 (1996), 2021-2027. MR 96i:32024
  • 2. B. Chen and J. Zhang, A study of the Bergman kernel and metric on non-smooth pseudoconvex domains, to appear in Science in China.
  • 3. K. Diederich and T. Ohsawa, A continuity principle for the Bergman kernel function, Publ. RIMS, Kyoto Univ. 28 (1992), 495-501. MR 93h:32030
  • 4. -, General continuity principles for the Bergman kernel, International Journal of Math. Vol 5, No. 2 (1994), 189-199. MR 95c:32023
  • 5. R.E. Greene and St.G. Krantz, Stability properties of the Bergman kernel and curvature properties of bounded domains, Study 100. Annals of Math. Princeton Univ Press (1981), 179-198. MR 83d:32023
  • 6. L. Hörmander, An introduction to complex analysis in several variables, Netherlands 1990. MR 91a:32001
  • 7. I. Ramadanov, Sur une propriete de la fonction de Bergman, C. R. Bulgare Sci. (1967), 759-762. MR 37:1632
  • 8. -, Some applications of the Bergman kernel to geometrical theory of functions, Complex Analysis, Banach Center Publications, Vol. 11 (1983), 275-286. MR 85h:32040

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32H10

Retrieve articles in all journals with MSC (1991): 32H10


Additional Information

Chen Boyong
Affiliation: Institute of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China
Address at time of publication: Department of Applied Mathematics, Tongji University,Shanghai 200092, People’s Republic of China

Zhang Jinhao
Affiliation: Department of Mathematics, Fudan University, Shanghai 200433, People’s Republic of China

DOI: https://doi.org/10.1090/S0002-9939-00-05333-8
Keywords: Bergman kernel
Received by editor(s): July 20, 1998
Received by editor(s) in revised form: October 30, 1998
Published electronically: February 29, 2000
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society