Several Complex Variables in China

Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics...

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Hauptverfasser: 楊, 重駿, 龔, 昇
Format: E-Book Buch
Sprache:Englisch
Veröffentlicht: Providence, Rhode Island American Mathematical Society 1993
Ausgabe:1
Schriftenreihe:Contemporary Mathematics
Schlagworte:
China
Functions of several complex variables
Mathematics
Mathematics > Research > China
ISBN:9780821851647, 0821851640
ISSN:0271-4132, 1098-3627
Online-Zugang:Volltext
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Abstract Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics covered are singular integrals, function spaces, differential operators, and factorization of meromorphic functions in several complex variables via analytic or geometric methods. Some results are reported in English for the first time.
AbstractList Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The present collection of survey and research articles comprises a current overview of research in several complex variables in China. Among the topics covered are singular integrals, function spaces, differential operators, and factorization of meromorphic functions in several complex variables via analytic or geometric methods. Some results are reported in English for the first time.
Author 龔, 昇
楊, 重駿
Author_FL キョウ, ショウ
ヨウ, チョウシュン
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Editor Gong, Sheng
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Snippet Today, there is increasing interest in complex geometry, geometric function theory, and integral representation theory of several complex variables. The...
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SubjectTerms China
Functions of several complex variables
Mathematics
Mathematics -- Research -- China
TableOfContents Complex geometry in China -- Biholomorphic mappings in several complex variables -- Global Łojasiewicz inequality, defect relation and applications of holomorphic curve theory -- Factorization of meromorphic functions in several complex variables -- Some results on singular integrals and function spaces in several complex variables -- Some results on the homogeneous Siegel domains in <inline-formula content-type="math/mathml"> C n \textbf {C}^n </inline-formula> -- Differential operators and function spaces -- Beltrami equation in high dimensions -- Singular integrals and integral representations in several complex variables
Intro -- Contents -- Preface -- Contributors -- Complex Geometry in China -- Biholomorphic Mappings in Several Complex Variables -- Introduction -- I. The conditions of starlikeness, convexity and univalency for a holomorphic mapping -- 1. The necessary and sufficient conditions of starlikeness for a holomorphic mapping on Reinhardt domain Dp -- 2. The necessary and sufficient conditions of starlikeness for a holomorphic mapping on Caratheodory complete domain -- 3. The sufficient condition of univalency for a locally biholomorphic mapping -- 4. The necessary and sufficient condition of convexity for holomorphic mapping -- II. Distortion theorem for biholomorphic mappings on transitive domains -- 1. Distortion theorem for the family of A-invariant mappings on the unit ball -- 2. Jacobian determinant of the biholomorphic mappings on transitive domains -- 3. Distortion theorem for the family of A-invariant mappings on bounded symmetric domains -- 4. Distortion theorem for the family of biholomorphic starlike mappings on bounded symmetric domains -- III. Growth theorem and covering theorem for biholomorphic starlike mappings -- 1. Growth theorem and covering theorem for biholomorphic starlike mappings on the unit ball -- 2. Growth theorem and covering theorem for biholomorphic starlike mappings on Reinhardt domain Bp -- 3. Growth theorem and covering theorem for biholomorphic starlike mappings on classical domains -- 4. Another growth theorem for biholomorphic starlike mappings on classical domains -- 5. Growth theorem and covering theorem for biholomorphic starlike mappings on Banach space -- IV. Biholomorphic convex mappings -- 1. Distortion theorem for biholomorphic convex mappings on bounded symmetric domains -- 2. Growth theorem and distortion theorem for biholomorphic convex mappings on the unit ball and on the Reinhardt domains
3. Growth theorem for biholomorphic convex mappings on bounded symmetric domains -- 4. Distortion theorem for biholomorphic convex mappings on bounded non-symmetric transitive domains -- 5. Distortion theorem for locally biholomorphic convex mappings on bounded symmetric domains -- V. Schwarzian derivatives -- 1. Schwarzian derivatives on classical domains -- 2. Schwarzian curvatures of holomorphic curves -- VI. The Bloch constant of holomorphic mappings on bounded symmetric domains -- 1. The Bloch constant of holomorphic mappings on the unit ball -- 2. The Bloch constant of holomorphic mappings on classical domains -- 3. The Bloch constant of holomorphic mappings on bounded symmetric domains -- References -- Global Lojasiewicz Inequality, Defect Relation and Applications of Holomorphic Curve Theory -- Factorization of Meromorphic Functions in Several Complex Variables -- Some Results on Singular Integrals and Function Spaces in Several Complex Variables -- Some Results on the Homogeneous Siegel Domains in Cn -- Differential Operators and Function Spaces -- Beltrami Equation in High Dimensions -- Singular Integrals and Integral Representations in Several Complex Variables -- I. Plemelj formulas with Bochner-Martinelli kernel and their applications -- 1. Plemelj formula with Bochner-Martinelli kernel -- 2. Singular integral equations on smooth closed manifolds -- 3. Holomorphic extension on Stein manifolds -- 4. ∂-closed extension of (p, q) differential forms in Cn -- 5. Plemelj formula in the case of piecewise smooth boundary -- 6. Finite part of singular integrals of Bochner-Martinelli type -- II. Integral representations in several complex variables -- 1. An integral formula on a bounded domain in Cn -- 2. Integral representation of (p, q) differential forms on real non-degenerate strictly pseudoconvex polyhedra on Stein manifolds
3. Integral representation of (p, q) differential forms with weight factors on complex manifolds -- 4. Fundamental solutions with weight factors of Cauchy-Riemann and induced Cauchy-Riemann operators on Stein manifolds
Title Several Complex Variables in China
URI https://www.ams.org/conm/142/
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Volume 142
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