About the Book
This three-volume set contains the proceedings of the Summer Research Institute on Several Complex Variables and Complex Geometry, held at the University of California at Santa Cruz in July 1989. The institute explored recent developments in the geometry and function theory of several complex variables. An attempt was made to stimulate interactions among the different methodologies in the subject, such as differential geometry, algebraic geometry, partial differential equations, harmonic analysis, and classical methods. The topics covered include function theory, complex geometry, partial differential equations, functional analysis, and analysis on manifolds. With contributions by some of the world's top experts in several complex variables and complex geometry, this book provides readers with insight into the current state of this field.
Table of Contents:
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 = 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 q2 /qz qz = 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-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.
