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84
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 MAPPINGS OF BALANCED DOMAINS IN Cn
"... Abstract. We extend a wellknown result, about the unit ball, by H. Alexander to a class of balanced domains in Cn, n> 1. Specifically: we prove that any proper holomorphic selfmap of a smoothly bounded balanced pseudoconvex domain of finite type in Cn, n> 1, is an automorphism. The main nove ..."
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Abstract. We extend a wellknown result, about the unit ball, by H. Alexander to a class of balanced domains in Cn, n> 1. Specifically: we prove that any proper holomorphic selfmap of a smoothly bounded balanced pseudoconvex domain of finite type in Cn, n> 1, is an automorphism. The main
PROPER HOLOMORPHIC MAPPINGS OF THE SPECTRAL UNIT BALL
, 704
"... Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2. L ..."
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Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2
PROPER HOLOMORPHIC MAPPINGS OF THE SPECTRAL UNIT BALL
, 704
"... Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2. L ..."
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Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2
PROPER HOLOMORPHIC MAPPINGS OF THE SPECTRAL UNIT BALL
"... Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2. L ..."
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Abstract. We prove an Alexander type theorem for the spectral unit ball Ωn showing that there are no nontrivial proper holomorphic mappings in Ωn, n ≥ 2. Let Mn denote the space of n × n complex matrices. In order to avoid some trivialities and ambiguities we assume in the whole paper that n ≥ 2
Publ. Mat. 45 (2001), 69–77 PROPER HOLOMORPHIC MAPPINGS BETWEEN RIGID POLYNOMIAL DOMAINS IN Cn+1
"... We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in Cn+1. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic selfmappings between such domains are biholomorphic. 1. ..."
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We describe the branch locus of proper holomorphic mappings between rigid polynomial domains in Cn+1. It appears, in particular, that it is controlled only by the first domain. As an application, we prove that proper holomorphic selfmappings between such domains are biholomorphic. 1.
RIGIDITY OF HOLOMORPHIC GENERATORS AND
"... ABSTRACT. In this paper we establish a rigidity property of holomorphic generators by using their local behavior at a boundary point of the open unit disk . Namely, if f 2 Hol(; C) is the generator of a oneparameter continuous semigroup fFtgt0, we show that the equality f(z) = o jz j3 when z! ..."
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! in each nontangential approach region at implies that f vanishes identically on . Note, that if F is a selfmapping of then f = I F is a generator, so our result extends the boundary version of the Schwarz Lemma obtained by D. Burns and S. Krantz. We also prove that two semigroups fFtgt0 and fGtgt0
Isolated fixed point sets for holomorphic maps
, 2006
"... Abstract We study discrete fixed point sets of holomorphic selfmaps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in C n with no nontrivial holomorphic retractions is construc ..."
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Abstract We study discrete fixed point sets of holomorphic selfmaps of complex manifolds. The main attention is focused on the cardinality of this set and its configuration. As a consequence of one of our observations, a bounded domain in C n with no nontrivial holomorphic retractions
Common fixed points of commuting holomorphic maps in the unit ball of C n .Proc.Amer.Math
 Soc
"... Abstract. Let Bn be the unit ball of Cn (n> 1). We prove that if f, g ∈ Hol(Bn,Bn) are holomorphic selfmaps of Bn such that f ◦ g = g ◦ f, then f and g have a common fixed point (possibly at the boundary, in the sense of Klimits). Furthermore, if f and g have no fixed points in Bn, then they ha ..."
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Cited by 6 (4 self)
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hyperbolic automorphisms of (the unit disk of C), two nontrivial commuting holomorphic selfmaps of have the same xed point in or the same \Wol point " in @.
Results 1  10
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