**Contemporary Mathematics**

Volume: 142;
1993;
173 pp;
Softcover

MSC: Primary 32;

Print ISBN: 978-0-8218-5164-7

Product Code: CONM/142

List Price: $47.00

AMS Member Price: $37.60

MAA Member Price: $42.30

**Electronic ISBN: 978-0-8218-7733-3
Product Code: CONM/142.E**

List Price: $47.00

AMS Member Price: $37.60

MAA Member Price: $42.30

# Several Complex Variables in China

Share this page *Edited by *
*Chung-Chun Yang; Sheng Gong*

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.

#### 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