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Functions of Several Complex Variables
1985In this chapter, we shall define holomorphic functions of several complex variables. The essentially local theory given in Chapter 1, §§3, 4 extends to these functions with little effort. We shall then prove two theorems which show that the behavior of functions of n complex variables, with n > 1, is, in some ways, radically different from that of ...
Raghavan Narasimhan, Yves Nievergelt
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The Schwarzian derivative in several complex variables IV [PDF]
Science in China Series A: Mathematics, 1998 The authors consider the Schwarzian derivative of a holomorphic \(n\times n\) matrix mapping \(W\) of an \(n\times n\) matrix variable \(Z\) along the direction \(Z\) and receive a necessary and sufficient condition of the transformation of this derivative to zero. [Part I: \textit{S. Gong} and \textit{C. H. FitzGerald}, Sci. China, Ser. A 36, No.
Sheng Gong, Qihuang Yu, Xue’an Zheng
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Several Complex Variables and Complex Geometry
1991David E Barrett, Uniqueness for the Dirilchlet problem for harmonic maps from the annulus into the space of planar discs Steve Bell, CR maps between hypersurfaces in Cn Carlos A Berenstein and Alain Yger, Bounds for the degrees in polynomial equations Thomas Bloom, Lagrange interpolants for entire functions on cn Urban Cegrell, An inequality for ...
Steven G. Krantz +3 more
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On Complex Analysis in Several Variables [PDF]
, 1997 In one dimension, every domain D ⊂ ℂ1 is a domain of holomorphy, that is, there is a holomorphic function f in D, f ∈ O(D) which cannot be holomorphically extended to larger domain because on the boundary ∂D of D f has a dense set of singularities. This fact was known already to Riemann and Weierstrass. For n > 1 the situation is quite different: Fritz
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What Is Several Complex Variables?
The American Mathematical Monthly, 1987expositor. Gail's excellence as a teacher at all levels is a corollary to a remarkable intellectual breadth and depth coupled with a rare sensitivity to the needs of his students. He has had nineteen Ph.D. students. The simple truth is that everything Gail has done-and he has done enormously much-has been well-done, useful, and important.
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Functions of Several Complex Variables
The American Mathematical Monthly, 1945(1945). Functions of Several Complex Variables. The American Mathematical Monthly: Vol. 52, No. 1, pp. 17-27.
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Normal theorems on several complex variables
Acta Mathematica Scientia, 2001The author proves that the limit of a sequence of \(K\)-quasimeromorphic mappings convergent on a simply connected closed domain \(D\) on a Riemann sphere \(V^m\) is a \(K\)-quasimeromorphic mapping from \(D\) to \(V^m\). By the method of covering surface, some normality theorems for a family of \(K\)-quasimeromorphic mappings of \(D\) are obtained.
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Lectures on Several Complex Variables
2014Preface.- Introduction.- Basics.- Cauchy Integral Formula.- Sequences of Holomorphic Functions.- Series.- Zero Sets of Holomorphic Functions.- Holomorphic Mappings.- Plurisubharmonic Functions.- The Dirichlet Problem.- Uniform Approximation.- Complex Manifolds.- Examples of Manifolds.- Holomorphic Continuation.- The Tangent Space.- Meromorphic ...
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Uniformization in Several Complex Variables
1991In this chapter we survey the current state of the theory of uniformization in several complex variables. In the case of one complex variable the uniformization theorem says that a simply connected Riemann surface is either the Riemann sphere ℙ1, or the open unit disk Δ or the Gaussian plane ℂ.
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