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PROPER HOLOMORPHIC MAPPINGS IN TETRABLOCK
, 2009
"... The theorem showing that there are no nontrivial proper holomorphic selfmappings in the tetrablock is proved. We obtain also some general extension results for proper holomorphic mappings and we prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes of ..."
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The theorem showing that there are no nontrivial proper holomorphic selfmappings in the tetrablock is proved. We obtain also some general extension results for proper holomorphic mappings and we prove that the Shilov boundary is invariant under proper holomorphic mappings between some classes
Proper holomorphic maps that must be rational
 Trans. Amer. Math. Soc
, 1984
"... Abstract. Suppose/: Dx » D2 is a proper holomorphic mapping between bounded domains in C". We shall prove that under certain circumstances/must be a rational mapping, i.e., that the n component functions/, of /are rational functions. Theorem 1. Suppose Dx is a bounded domain in C " whose ..."
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Cited by 1 (1 self)
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Abstract. Suppose/: Dx » D2 is a proper holomorphic mapping between bounded domains in C". We shall prove that under certain circumstances/must be a rational mapping, i.e., that the n component functions/, of /are rational functions. Theorem 1. Suppose Dx is a bounded domain in C " whose
THE BERGMAN KERNEL FUNCTION AND PROPER HOLOMORPHIC MAPPINGS
, 1982
"... It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function un ..."
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Cited by 9 (1 self)
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It is proved that a proper holomorphic mapping / between bounded complete Reinhardt domains extends holomorphically past the boundary and that if, in addition, /~'(0) = {0}, then / is a polynomial mapping. The proof is accomplished via a transformation rule for the Bergman kernel function
Proper Holomorphic Maps between Reinhardt Domains In C²
, 2004
"... We characterize pairs of bounded Reinhardt domains in C² between which there exists a proper holomorphic map and find all proper maps that are not elementary algebraic. ..."
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Cited by 3 (0 self)
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We characterize pairs of bounded Reinhardt domains in C² between which there exists a proper holomorphic map and find all proper maps that are not elementary algebraic.
PROPER HOLOMORPHIC MAPPINGS BETWEEN REINHARDT DOMAINS IN C²
, 2008
"... We describe all possibilities of existence of nonelementary proper holomorphic maps between nonhyperbolic Reinhardt domains in C² and the corresponding pairs of domains. ..."
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We describe all possibilities of existence of nonelementary proper holomorphic maps between nonhyperbolic Reinhardt domains in C² and the corresponding pairs of domains.
FACTORIZATION OF PROPER HOLOMORPHIC MAPPINGS THROUGH THULLEN DOMAINS
"... Given a bounded domain in C 2 and a proper holomorphic mapping onto the unit ball in C 2, we give a criterion for a proper mapping to factor through Thullen domains by its branch locus. As an application, we present a characterization of the Thullen domains among bounded domains admitting a proper h ..."
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Cited by 3 (2 self)
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Given a bounded domain in C 2 and a proper holomorphic mapping onto the unit ball in C 2, we give a criterion for a proper mapping to factor through Thullen domains by its branch locus. As an application, we present a characterization of the Thullen domains among bounded domains admitting a proper
A note on pseudoconvexity and proper holomorphic mappings
 Proc. A.M.S
, 1988
"... ABSTRACT. In this paper we discuss some connections between proper holomorphic mappings between domains in Cn and the boundary behaviors of certain canonical invariant metrics. A compactness theorem has been proved. This generalizes slightly an earlier result proved by the second author. Introductio ..."
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Cited by 1 (1 self)
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ABSTRACT. In this paper we discuss some connections between proper holomorphic mappings between domains in Cn and the boundary behaviors of certain canonical invariant metrics. A compactness theorem has been proved. This generalizes slightly an earlier result proved by the second author
On critical points of proper holomorphic maps on the unit disk
 Department of Mathematics, SUNY at Stony Brook, NY 11794 Email address: zakeri@math.sunysb.edu
, 1998
"... Abstract. We prove that a proper holomorphic map on the unit disk in the complex plane is uniquely determined up to postcomposition with a Möbius transformation by its critical points. This note will give a brief proof of the following known theorem: Theorem 1. Let c1, · · · , cd be given (not n ..."
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Cited by 10 (1 self)
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Abstract. We prove that a proper holomorphic map on the unit disk in the complex plane is uniquely determined up to postcomposition with a Möbius transformation by its critical points. This note will give a brief proof of the following known theorem: Theorem 1. Let c1, · · · , cd be given (not
Results 1  10
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6,452