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 Advanced Studies in Pure Mathematics 2004; 360 pp; hardcover Volume: 42 ISBN-10: 4-931469-27-2 ISBN-13: 978-4-931469-27-3 List Price: US$92 Member Price: US$73.60 Order Code: ASPM/42 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. 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. Volumes in this series are freely available electronically 5 years post-publication. Published for the Mathematical Society of Japan by Kinokuniya, Tokyo, and distributed worldwide, except in Japan, by the AMS. Readership 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 T. Nishino -- Mathematics of Professor Oka--a landscape in his mind Y. Aihara -- Uniqueness problem for meromorphic mappings under conditions on the preimages of divisors T. Akahori -- On the middle dimension cohomology of $$A_1$$ singularity T. Aoki, T. Kawai, and Y. Takei -- The exact steepest descent method--a new steepest descent method based on the exact WKB analysis E. Bedford -- Excursions of a complex analyst into the realm of dynamical systems J. El Goul -- Demailly's 2-jet negativity of certain hyperbolic fibrations J. E. Fornæss -- Short $$C^k$$ H. Fujimoto -- Some constructions of hyperbolic hypersurfaces in $${P^n}(C)$$ K. Hirachi -- A link between the asymptotic expansions of the Bergman kernel and the Szegö kernel A. Iordan -- On the non-existence of smooth Levi-flat hypersurfaces in $$CP_n$$ S.-J. Kan -- Recent development on Grauert domains K.-T. Kim -- Analytic polyhedra with non-compact automorphism group S. Kobayashi -- Problems related to hyperbolicity of almost complex structures J. J. Kohn -- Ideals of multipliers G. Komatsu -- The Bergman kernel of Hartogs domains and transformation laws for Sobolev-Bergman kernels M. Kuranishi -- An approach to the Cartan geometry II: CR manifolds L. Lempert -- The $$\bar{\partial}$$ equation in $$N$$ variables, as $$N$$ varies K. Matsumoto -- Levi form of logarithmic distance to complex submanifolds and its application to developability Y. Miyaoka -- Numerical characterisations of hyperquadrics S. Mori -- Meromorphic mappings and deficiencies J. Noguchi -- Intersection multiplicities of holomorphic and algebraic curves with divisors T. Ohsawa -- Generalization of a precise $$L^2$$ division theorem M. Passare -- Amoebas, convexity and the volume of integer polytopes R. M. Range -- On the decomposition of holomorphic functions by integrals and the local CR extension theorem O. Riemenschneider -- The monodromy covering of the versal deformation of cyclic quotient surface singularities G. Schumacher -- Moduli as algebraic spaces S. Shimizu -- Prolongation of holomorphic vector fields on a tube domain and its applications M. Shirosaki -- Hypersurfaces and uniqueness of holomorphic mappings S. Takayama -- Seshadri constants and a criterion for bigness of pseudo-effective line bundles H. Tsuji -- Subadjunction theorem T. Ueda -- Fixed points of polynomial automorphisms of $$C^n$$ K. Yamanoi -- On Nevanlinna theory for holomorphic curves in abelian varieties S.-T. Yau -- Numerical characterization for affine varieties be a cone over nonsingular projective varieties K.-I. Yoshikawa -- Nikulin's $$K$$3 surfaces, adiabatic limit of equivariant analytic torsion, and the Borcherds $$\Phi$$-function