On hyperbolicity and tautness modulo an analytic subset of Hartogs domains-Reference-Cited by-同舟云学术

On hyperbolicity and tautness modulo an analytic subset of Hartogs domains

Published:2013-07-09 Issue:10 Volume:141 Page:3623-3631
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Thai Do,Thomas Pascal,Trao Nguyen,Duc Mai

Abstract

Let X X be a complex space and H H a positive homogeneous plurisubharmonic function H H on X × C m X\times \mathbb {C}^m . Consider the Hartogs-type domain Ω H ( X ) := { ( z , w ) ∈ X × C m : H ( z , w ) > 1 } \Omega _{H}(X):=\{(z,w)\in X\times \mathbb {C}^m:H(z,w)>1 \} . Let S S be an analytic subset of X X . We give necessary and sufficient conditions for hyperbolicity and tautness modulo S × C m S\times \mathbb {C}^m of Ω H ( X ) \Omega _{H}(X) , with the obvious corollaries for the special case of Hartogs domains.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/2013-141-10/S0002-9939-2013-11645-X/S0002-9939-2013-11645-X.pdf

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