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On hyperbolicity and tautness modulo an analytic subset of Hartogs domains


Authors: Do Duc Thai, Pascal J. Thomas, Nguyen Van Trao and Mai Anh Duc
Journal: Proc. Amer. Math. Soc. 141 (2013), 3623-3631
MSC (2010): Primary 32F45; Secondary 32C25, 32H25, 32Q45
DOI: https://doi.org/10.1090/S0002-9939-2013-11645-X
Published electronically: July 9, 2013
MathSciNet review: 3080184
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Abstract: Let $ X$ be a complex space and $ H$ a positive homogeneous plurisubharmonic function $ H$ on $ X\times \mathbb{C}^m$. Consider the Hartogs-type domain $ \Omega _{H}(X):=\{(z,w)\in X\times \mathbb{C}^m:H(z,w)<1 \}$. Let $ S$ be an analytic subset of $ X$. We give necessary and sufficient conditions for hyperbolicity and tautness modulo $ S\times \mathbb{C}^m$ of $ \Omega _{H}(X)$, with the obvious corollaries for the special case of Hartogs domains.


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Additional Information

Do Duc Thai
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy str., Hanoi, Vietnam
Email: ducthai.do@gmail.com

Pascal J. Thomas
Affiliation: Université de Toulouse, UPS, INSA, UT1, UTM, Institut de Mathématiques de Toulouse, F-31062 Toulouse, France
Email: pascal.thomas@math.univ-toulouse.fr

Nguyen Van Trao
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy str., Hanoi, Vietnam
Email: ngvtrao@yahoo.com

Mai Anh Duc
Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy str., Hanoi, Vietnam
Email: ducphuongma@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11645-X
Keywords: Hyperbolicity modulo an analytic subset, tautness modulo an analytic subset, Hartogs domains
Received by editor(s): December 18, 2011
Received by editor(s) in revised form: January 6, 2012
Published electronically: July 9, 2013
Additional Notes: The research of the authors was supported by an NAFOSTED grant of Vietnam and by an ARCUS cooperation program with the support of the Régions Ile-de-France and Midi-Pyrénées
Communicated by: Franc Forstneric
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.