Geometry of Holomorphic Mappings

Chapter. 1. Preliminaries.- Chapter. 2. Why boundary regularity?.- Chapter. 3. Continuous extension of holomorphic mappings.- Chapter. 4. Boundary smoothness of holomorphic mappings.- Chapter. 5. Proper holomorphic mappings.- Chapter. 6. Uniformization of domains with large automorphism groups.- Chapter. 7. Local equivalence of real analytic hypersurfaces.- Chapter. 8. Geometry of real hypersurfaces: analytic continuation.- Chapter. 9. Segre varieties.- Chapter. 10. Holomorphic correspondences.- Chapter. 11. Extension of proper holomorphic mappings.- Chapter. 12. Extension in C2.- Appendix.- Bibliography.- Index.

Sergey Pinchuk graduated from Moscow State University in 1971. He received his PhD (Candidate in Math) in 1974 and habilitation (Doctor of Sciences) in 1980 also from Moscow State University. He is currently a professor at Indiana University. His main work is dedicated to several complex variables. Sergey Pinchuk was an invited plenary speaker at the International Congress of Mathematicians in 1983 and 1998.

Rasul Shafikov received PhD in Mathematics in 2001 at Indiana University under the supervision of Sergey Pinchuk. He was a post-doc at Stony Brook University, New York, and a visiting scholar at the Max Planck Math Institute in Bonn, Germany. Since 2004 he is a professor at the University of Western Ontario, Canada. Rasul Shafikov is the author of over 40 papers in the area of several complex variables, complex geometry and dynamical systems.

Alexandre Sukhov was born in Ufa (Russia) in 1964. He received PhD at the Institute of Mathematics of the Russian Academy of Sciences in Ufa, 1989. From 1995 to 1999 he was maitre de conferences at the University Aix-Marseille-1. He received HDR (habilitation à diriger des recherches) from this university. From 1999 Alexandre Sukhov is a professor at the University of Lille. Alexandre Sukhov is the author of over 80 papers in complex analysis and adjacent areas, such as the non-linear analysis, PDE and symplectic geometry.