# Several Complex Variables in China

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*Chung-Chun Yang; Sheng Gong*

#### Readership

Graduate students and specialists.

# Table of Contents

## Several Complex Variables in China

- Contents v6 free
- Preface vii8 free
- Contributors xi12 free
- Complex Geometry in China 114 free
- Biholomorphic Mappings in Several Complex Variables 1528
- Introduction 1629
- I. The conditions of starlikeness, convexity and univalency for a holomorphic mapping 1831
- 1. The necessary and sufficient conditions of starlikeness for a holomorphic mapping on Reinhardt domain Dp 1831
- 2. The necessary and sufficient conditions of starlikeness for a holomorphic mapping on Caratheodory complete domain 1932
- 3. The sufficient condition of univalency for a locally biholomorphic mapping 2134
- 4. The necessary and sufficient condition of convexity for holomorphic mapping 2336

- II. Distortion theorem for biholomorphic mappings on transitive domains 2336
- 1. Distortion theorem for the family of A-invariant mappings on the unit ball 2336
- 2. Jacobian determinant of the biholomorphic mappings on transitive domains 2538
- 3. Distortion theorem for the family of A-invariant mappings on bounded symmetric domains 2740
- 4. Distortion theorem for the family of biholomorphic starlike mappings on bounded symmetric domains 2841

- III. Growth theorem and covering theorem for biholomorphic starlike mappings 2942
- 1. Growth theorem and covering theorem for biholomorphic starlike mappings on the unit ball 2942
- 2. Growth theorem and covering theorem for biholomorphic starlike mappings on Reinhardt domain Bp 3043
- 3. Growth theorem and covering theorem for biholomorphic starlike mappings on classical domains 3144
- 4. Another growth theorem for biholomorphic starlike mappings on classical domains 3245
- 5. Growth theorem and covering theorem for biholomorphic starlike mappings on Banach space 3245

- IV. Biholomorphic convex mappings 3346
- 1. Distortion theorem for biholomorphic convex mappings on bounded symmetric domains 3346
- 2. Growth theorem and distortion theorem for biholomorphic convex mappings on the unit ball and on the Reinhardt domains 3548
- 3. Growth theorem for biholomorphic convex mappings on bounded symmetric domains 3750
- 4. Distortion theorem for biholomorphic convex mappings on bounded non-symmetric transitive domains 3851
- 5. Distortion theorem for locally biholomorphic convex mappings on bounded symmetric domains 3952

- V. Schwarzian derivatives 4053
- VI. The Bloch constant of holomorphic mappings on bounded symmetric domains 4356
- References 4659

- Global Lojasiewicz Inequality, Defect Relation and Applications of Holomorphic Curve Theory 4962
- Factorization of Meromorphic Functions in Several Complex Variables 6174
- Some Results on Singular Integrals and Function Spaces in Several Complex Variables 7588
- Some Results on the Homogeneous Siegel Domains in Cn 103116
- Differential Operators and Function Spaces 121134
- Beltrami Equation in High Dimensions 143156
- Singular Integrals and Integral Representations in Several Complex Variables 151164
- I. Plemelj formulas with Bochner-Martinelli kernel and their applications 151164
- 1. Plemelj formula with Bochner-Martinelli kernel 151164
- 2. Singular integral equations on smooth closed manifolds 155168
- 3. Holomorphic extension on Stein manifolds 157170
- 4. ∂-closed extension of (p, q) differential forms in Cn 158171
- 5. Plemelj formula in the case of piecewise smooth boundary 160173
- 6. Finite part of singular integrals of Bochner-Martinelli type 161174

- II. Integral representations in several complex variables 162175
- 1. An integral formula on a bounded domain in Cn 162175
- 2. Integral representation of (p, q) differential forms on real non-degenerate strictly pseudoconvex polyhedra on Stein manifolds 165178
- 3. Integral representation of (p, q) differential forms with weight factors on complex manifolds 168181
- 4. Fundamental solutions with weight factors of Cauchy-Riemann and induced Cauchy-Riemann operators on Stein manifolds 171184