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)

 
 

 

Complex retractions and envelopes of holomorphy


Author: S. Trapani
Journal: Proc. Amer. Math. Soc. 104 (1988), 145-148
MSC: Primary 32D10; Secondary 32E15
DOI: https://doi.org/10.1090/S0002-9939-1988-0958057-X
MathSciNet review: 958057
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we show that if a domain $ \Omega $ of a Stein manifold $ X$ is a "holomorphic deformation retract" of a domain of holomorphy $ D \subseteq X$, then $ \Omega $ has a univalent envelope of holomorphy $ {\Omega ^*} \subseteq X$.


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

  • [1] B. Almer, Sur quelques problèmes de la théorie..., Arkiv für Mat. Astronomy och Fysik B.d. 17 (7) (1922).
  • [2] S. Bochner and W. T. Martin, Several complex variables, Princeton Univ. Press, Princeton, N. J., 1948, 366. MR 0027863 (10:366a)
  • [3] R. Carmignani, Envelope of holomorphy and holomorphic convexity, Trans. Amer. Math. Soc. 179 (1973), 415-431. MR 0316748 (47:5296)
  • [4] S. Coen, Una introduzione ai domini di Riemann non ramificati $ n$ dimensionali, Pitagora Ed., Bologna, 1980.
  • [5] J. E. Fornaess and W. H. Zame, Riemann domains and envelopes of holomorphy, Duke Math. J. 50 (1983), 273-283. MR 700141 (84i:32017)
  • [6] R. Gunning and H. Rossi, Analytic functions of several complex variables, Prentice-Hall, 1965. MR 0180696 (31:4927)
  • [7] L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, 1966. MR 0203075 (34:2933)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 32D10, 32E15

Retrieve articles in all journals with MSC: 32D10, 32E15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0958057-X
Article copyright: © Copyright 1988 American Mathematical Society

American Mathematical Society