Several Complex Variables in China.

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.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.