Complex Analysis in Several Variables: Memorial Conference of Kiyoshi Oka's Centennial Birthday, Kyoto/Nara 2001

This volume resulted from a conference held at Kyoto University and Nara Women's University (Japan) in commemoration of the late Professor Kiyoshi Oka, one of the most famous Japanese mathematicians. Included are 34 research and survey papers contributed by the invited lecturers and a letter written for the occasion by H. Cartan. Among the leading mathematicians who contributed to the volume are E. Bedford, S. Kobayashi, J. J. Kohn, and M. Kuranishi. The topics discussed include pseudoconvex domains, $\bar{\partial}$ analysis (including $L^2$ theory), the Bergman kernel, value distribution theory, hyperbolic manifolds, dynamical systems, infinite dimensional complex analysis, algebraic analysis, CR structure, singularity theory, algebraic geometry, and others. The book is suitable for advanced graduate students and research mathematicians interested in complex analysis, algebraic geometry, and complex geometry.

Table of Contents:
Part I: Photos of Kiyoshi Oka Oka, Kiyoshi Memorial conference of Kiyoshi Oka's centennial birthday on complex analysis in several variables, Kyoto/Nara 2001 Message from Professor Henri Cartan Part II: Mathematics of Professor Oka--a landscape in his mind by T. Nishino Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors by Y. Aihara On the middle dimension cohomology of $A_1$ singularity by T. Akahori The exact steepest descent method-a new steepest descent method based on the exact WKB analysis by T. Aoki, T. Kawai, and Y. Takei Excursions of a complex analyst into the realm of dynamical systems by E. Bedford Demailly's 2-jet negativity of certain hyperbolic fibrations by J. El Goul Short $C^k$ by J. E. Fornaess Some constructions of hyperbolic hypersurfaces in ${P^n}(C)$ by H. Fujimoto A link between the asymptotic expansions of the Bergman kernel and the Szego kernel by K. Hirachi On the non-existence of smooth Levi-flat hypersurfaces in $CP_n$ by A. Iordan Recent development on Grauert domains by S.-J. Kan Analytic polyhedra with non-compact automorphism group by K.-T. Kim Problems related to hyperbolicity of almost complex structures by S. Kobayashi Ideals of multipliers by J. J. Kohn The Bergman kernel of Hartogs domains and transformation laws for Sobolev-Bergman kernels by G. Komatsu An approach to the Cartan geometry II: CR manifolds by M. Kuranishi The $\bar{\partial}$ equation in $N$ variables, as $N$ varies by L. Lempert Levi form of logarithmic distance to complex submanifolds and its application to developability by K. Matsumoto Numerical characterisations of hyperquadrics by Y. Miyaoka Meromorphic mappings and deficiencies by S. Mori Intersection multiplicities of holomorphic and algebraic curves with divisors by J. Noguchi Generalization of a precise $L^2$ division theorem by T. Ohsawa Amoebas, convexity and the volume of integer polytopes by M. Passare On the decomposition of holomorphic functions by integrals and the local CR extension theorem by R. M. Range The monodromy covering of the versal deformation of cyclic quotient surface singularities by O. Riemenschneider Moduli as algebraic spaces by G. Schumacher Prolongation of holomorphic vector fields on a tube domain and its applications by S. Shimizu Hypersurfaces and uniqueness of holomorphic mappings by M. Shirosaki Seshadri constants and a criterion for bigness of pseudo-effective line bundles by S. Takayama Subadjunction theorem by H. Tsuji Fixed points of polynomial automorphisms of $C^n$ by T. Ueda On Nevanlinna theory for holomorphic curves in abelian varieties by K. Yamanoi Numerical characterization for affine varieties be a cone over nonsingular projective varieties by S.-T. Yau Nikulin's $K$3 surfaces, adiabatic limit of equivariant analytic torsion, and the Borcherds $\Phi$-function by K.-I. Yoshikawa.