Several Complex Variables and Complex Geometries, Parts 1-3

The proceedings of the July 1989 course are presented in three volumes with a total of 98 contributions on such topics as: mappings of strongly pseudoconvex Cauchy-Riemann manifolds; rational curves and extensions of holomorphic mappings; complex analysis in tube cones, some aspects of weakly pseudoconvex domains; invariants of CR densities; characterization of affine varieties; operator theory on Reinhardt domains; and the regularity of coanalytic Toeplitz operators. No index. Annotation copyright Book News, Inc. Portland, Or.

David E Barrett, Uniqueness for the Dirilchlet problem for harmonic maps from the annulus into the space of planar discs; Steve Bell, CR maps between hypersurfaces in Cn; Carlos A Berenstein and Alain Yger, Bounds for the degrees in polynomial equations; Thomas Bloom, Lagrange interpolants for entire functions on cn; Urban Cegrell, An inequality for analytic functions; J A Cima and W R Derrick, Some solutions of the Beltrami equation with J Jµ J J ? = 1; V Ezhov, On the problem of the linearization of the stability group of real-analytic hypersurface; Franc Forstneric, Mappings of strongly pseudoconvex Cauchy-Reimann manifolds; S M Ivashkovich, Rational curves and extensions of holomorphic mappings; Jacob Korevaar, Applications of Cn capacities; Steven G Krantz, Convexity in complex analysis; Donna Kumagai, Solutions of q2µ/ qz q~z = e2u and analytic multivalued functions; Alan Noell, Local versus global convexity of pseudoconvex domains; Sergey Pinchuk, The scaling method and holomorphic mappings; Evgeny A Poletsky, Plurisubharmonic functions as solutions of variational problems; A G Sergeev, On complex analysis in tube cones; Bernard Shiffman, Separately meromorphic functions and separately holomorphic mappings; Nessim Sibony, Some aspects of weakly pseudoconvex domains; Pascal J Thomas, Unions minimales de n-plans reels d'enveloppe egala a Cn; Jan Wiegerinck and Rein Zeinstra, Separately subharmonic functions; When are they subharmonic; Kehe Zhu, Functions of bounded mean oscillation in the Bergman metric on bounded symmetric domains. PART II Robert E Greene, The geometry of complex manifolds; An overview; Marco Abate, Angular derivatives in strongly pseudoconvex domains; Yukinobu Adachi and Masakazu Suzuki, Degeneracy points of the Kobayashi pseudodistances on complex manifolds; Takao Akahori, On the construction of the moduli space for strongly pseudoconvex domains; Andrew Balas, On the holomorphic sectional curvature of complete domains in Cn that are not Stein; J Bland and T Duchamp, Normal forms for convex domains; Ciprian Borcea, Homogenous vector bundles and families of Calabi-Yau threefolds. II; Jean Pierre Demailly, Holomorphic Morse inequalities; Pierre Dolbeault, Some problems; Michael G Eastwood and C Robin Graham, Invariants of CR densities; Yakov Eliashberg and Mikhael Gromov, Convex symplectic manifolds; H R Fischer and R J Fisher, Jr, Simple partial connections and the Einstein conditions; Sidney Frankel, Applications of affine geometry to geometric function theory in several complex variables Part 1. Convergent rescalings and intrinsic quasi-isometric structure; Akito Futaki, A Lie algebra character and Kahler-Einstein metrics of positive scalar curvature; Bruce Gilligan, On the ends of complex manifolds homogenous under a Lie group; James F Glazebrook and Franz W Kamber, Determinant line bundles for Hermitian foliations and a generalized Quillen metric; Ian Graham, Sharp constants for the Koebe theorem and for estimates of intrinsic metrics on convex domains; Chong-Kyu Han, Rigid immersions of G-structures and analyticity of CR mappings into spheres; J William Helton and Orlando Merino, Optimal analytic disks; Marek Jarnicki and Peter Pflug, Some remarks on the product property for invariant pseudometrics; Shanyu Ji, Smoothing of currents and Moisezon manifolds; Kang-Tae Kim, Biholomorphic mappings between quasicircular domains in Cn; Akio Kodama, Characterizations of certain weakly pseudoconvex domains in Cn from the viewpoint of biholomorphic automorphism groups; Claude LeBrun, Complete Ricci-flat Kahler metrics on Cn need not be flat. Steven Shin-Yi Lu, On meromorphic maps into varieties of log-general type; Ngaiming Mok, Aspects of Kahler geometry on arithmetic varieties; J Noguchi, Moduli spaces of holomorphic mappings into hyperbolic spaces and its applications; Salomon Ofman, The analytic Radon transform; Takeo Ohsawa, Applications of the q technique in L2 Hodge theory on complete Kahler manifolds; Marius Overholt, Bounds on the derivates of holomorphic endomorphisms; Giorgio Patrizio and Pit-Mann Wong, Monge-Ampere functions with large center; Mathias Peternell, A characterization of affine varieties; Thomas Peternell and Michael Schneider, Compactifications of Cn: A survey; T Ratiu and A Todorov, An infinite-dimensional point of view on the Weil-Petersson metric; Min Ru and Wilhelm Stoll, The Cartan conjecture for moving targets; Morihiko Saito, On Kollar's conjecture; Leslie Saper and Steven Zucker, An introduction to L2-cohomology; Vo Van Tan, On the compactfication problems for Stein 3-folds; Gang Tian, On one of Calabi's problems; T Tonev, Multi-dimensional analytic structures and uniform algebras; J Varouchas, The q q-equation on complex spaces; Jean-Pierre Vigue, Fixed points of holomorphic mappings in a bounded convex domain in Cn; L Waelbroeck, Holomorphic functions taking their values in a q-space and the Cauchy-Fantappie formula; B Wong, Schwarz's lemma and Hermitian manifolds with constant holomorphic curvature; H Wu, Polynomial functions on complete Kahler manifolds; Kichoon Yang, The Chern numbers of projective algebraic hypersurfaces; Shing-Tung Yau, A review of complex differential geometry. Part III. M S Baouendi and Linda Preiss Rothschild, Minimality and the extension of functions from generic manifolds; M S Baouendi and Linda Preiss Rothschild, Holomorphic mappings of real analytic hypersurfaces; David Catlin, Extension of CR structures; Der-Chen E Chang and Steven G Krantz, hp regularities for NIS operators on weakly pseudo-convex domains of finite type in C2; So-Chin Chen, Global regularity of the q-Neumann problem in dimension two; Michael Christ, On the qb equation for three-dimensional CR manifolds; Paulo Cordaro and Francois Treves, Necessary conditions for the local solvability of the tangential CR equations; Raul Curto, Operator theory on Reinhardt domains; John P D'Angelo, Finite type and the intersection of real and complex subvarieties; Makhlouf Derridj and David s Tartakoff, Local analyticity for the q-Neumann problem and for &b in some model domains without maximal estimates; John Erik Fornaess and Nessim Sibony, On Lp estimates for q; Daryl Geller, Approximate projections and analytic pseudolocality of the Szego projection on domains in C2; Pengfei Guan, On an example of a subelliptic boundary value problem; Gary A Harris, Degenerate surfaces in C2; C Denson Hill, Counterexamples to Newlander-Nirenberg up to the boundary; A Alexandrou Himonas, Finite type analytic partial differential operators and analytic hypoellipticity; D Khavinson, Singularities of harmonic functions in Cn; Christer O Kiselman, A study of the Bergman projections in certain Hartogs domains; Masatake Kuranishi, The frame bundles of CR structures and the Bergman kernel (I); Christine Laurent-Thiebaut, Resolution du qb a support compact et phenomene de Hartogs-Bochner dans les varieties CR; Ewa Ligocka, On the regularity of coanalytic Toeplitz operators; Hing-Sun Luk and Stephen S-T Yau, Obstructions to embedding of real (2n-1)-dimensional compact CR manifolds in Cn+1; Jeffrey D McNeal, On sharp Holder estimates for the solutions of the q-equations; Reinhold Meise, B A Taylor, and Dietmar Vogt, Equivalence of analytic and plurisubharmonic Phragmen-Lindelof conditions; John C Polking, The Cauchy-Reimann equations in convex domains; Jean-Pierre Rosay, Examples of smooth CR structures with only nonsmooth CR functions; Norberto Salinas, Noncompactness of the q-Neumann problem and Toeplitz C*-algebras; Mei-Chi Shaw, Local solvability and estimates for qb on CR manifolds; Nancy K Stanton, Rigid hypersurfaces in C2; S M Webster, The integrability problem for CR vector bundles.