Geometric Complex Analysis

Proceedings of the Third International Research Institute of Mathematical Society of Japan

Third International Research Institute of Mathematical Society of Japan

, Hayama, Japan

, 19 – 29 March 1995

https://doi.org/10.1142/2911 | July 1996

Pages: 736

Edited by:
J Noguchi (Tokyo Institute of Technology, Japan),
H Fujimoto (Kanazawa University, Japan),
J Kajiwara (Kyushu University, Japan), and
T Ohsawa (Nagoya University, Japan)

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ISBN: 978-981-4548-59-5 (ebook) USD 47.00 Add to cart

This proceedings is a collection of articles in several complex variables with emphasis on geometric methods and results, which includes several survey papers reviewing the development of the topics in these decades. Through this volume one can see an active field providing insight into other fields like algebraic geometry, dynamical systems and partial differential equations.

Contents:

Compositional Roots of Hénon Maps (G T Buzzard & J E Fornaess)
A Progress Report on Analytic Hypoellipticity (M Christ)
Some Aspects of the Levi Problem: Recent Developments (K Diederich)
Complex Analysis in an Infinite Dimensional Setting (S Dineen)
CR Structures and Tubular Complex Neighborhoods (M Kuranishi)
Holomorphic Foliations with Compatible Degenerate Kähler Metrics: Applications to the Shafarevich Conjecture and to Fibration Theorems (N Mok)
The Fujita Conjecture and the Extension Theorem of Ohsawa-Takegoshi (Y T Siu)
On a Problem of Ohsawa (M Tsuji)
and other papers

Readership: Graduate students in mathematics and mathematicians.

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Geometric Complex Analysis: Third International Research Institute of Mathematical Society of Japan

Pages:1–738

https://doi.org/10.1142/9789814532143

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The Table of Contents for the book is as follows:

PREFACE
OTHER TALKS
LIST OF ORGANIZING COMMITTEE
LIST OF PARTICIPANTS
LEFSCHETZ TYPE THEOREM
CONTINUATION OF HOLOMORPHIC FUNCTIONS FROM SUBVARIETIES
ON HODGE THEORY OVER STRONGLY PSEUDO CONVEX BOUNDARIES
GROMOV'S METHOD AND HULLS
DEGENERATE ELLIPTIC OPERATORS, H¹ SPACES AND DIFFUSIONS ON STRONGLY PSEUDOCONVEX DOMAINS
THE PLURI-COMPLEX GREEN FUNCTION AND A COVERING MAPPING
RESIDUE CURRENTS AND ARITHMETICAL APPLICATIONS
A SPLITTING PROPERTY FOR PROPER HOLOMORPHIC MAPPINGS BETWEEN REINHARDT DOMAINS
COMPOSITIONAL ROOTS OF HÉNON MAPS
SOME REMARKS ON THE PLURICOMPLEX GREEN FUNCTION
CONSTRUCTION OF EQUILIBRIUM CURRENT DENSITIES
ON ZERO SETS OF HOLOMORPHIC FUNCTIONS IN HARDY CLASSES
ESTIMATES ON THE BERGMAN KERNELS ON SOME DOMAINS IN Cⁿ
NUMERICAL RADIUS OF A HOLOMORPHIC MAPPING
A PROGRESS REPORT ON ANALYTIC HYPOELLIPTICITY
EXAMPLES OF PLANE CURVES OF LOW DEGREES WITH HYPERBOLIC AND C-HYPERBOLIC COMPLEMENTS
SOME ASPECTS OF THE LEVI PROBLEM: RECENT DEVELOPMENTS
COMPLEX ANALYSIS IN AN INFINITE DIMENSIONAL SETTING
A BIMEROMORPHIC CHARACTERIZATION OF COMPACT COMPLEX PARALLELIZABLE MANIFOLDS
PARTIAL COMPACTIFICATIONS OF CERTAIN HYPERKÄHLER QUOTIENTS
VALUE-DISTRIBUTION-THEORETIC PROPERTIES OF THE GAUSS MAP OF COMPLETE MINIMAL SURFACES
ON THE BLOCH CONSTANT FOR CONVEX MAPS OF THE UNIT BALL IN Cⁿ
PROPER HOLOMORPHIC SELF MAPPINGS OF SOME REINHARDT DOMAINS IN Cⁿ
ON PROPER HOLOMORPHIC MAPPINGS AND CR MAPPINGS
INVARIANTS OF CR STRUCTURES AND THE LOGARITHMIC SINGULARITY OF THE BERGMAN KERNEL
THE EXISTENCE OF SOLUTIONS OF THE -PROBLEM ON AN INFINITE DIMENSIONAL RIEMANN DOMAIN
ACTIONS OF GROUPS OF BIRATIONALLY EXTENDIBLE AUTOMORPHISMS
A NEW CONSTRUCTION OF AN ASYMPTOTICS FOR THE FUNDAMENTAL SOLUTION FOR PARABOLIC INITIAL-BOUNDARY PROBLEM AND ITS APPLICATION TO THE -NEUMANN PROBLEM
COMPACTIFICATIONS OF SYMMETRIC SPACES AND LOCALLY SYMMETRIC SPACES
NEW APPROACHES TO THE RIEMANN MAPPING THEOREM
REPRODUCING KERNELS FOR ABSTRACT WIENER SPACES
LIOUVILLE THEOREMS BASED ON DIRICHLET INTERGALS
ON HANKEL OPERATOR
RESTRUCTURING VALUE DISTRIBUTION THEORY
ON THE INTRINSIC RELATIVE DISTANCE
CHARACTERIZATIONS OF GENERALIZED COMPLEX ELLIPSOIDS IN Cⁿ FROM THE VIEWPOINT OF BIHOLOMORPHIC AUTOMORPHISMS
CR STRUCTURES AND TUBULAR COMPLEX NEIGHBORHOODS
FROM LOCAL TO GLOBAL HOMOTOPY FORMULAS AND
ALGEBRAIC APPROXIMATIONS
ON HYPERBOLICITY AND THE GREEN-GRIFFITHS CONJECTURE FOR SURFACES
ORTHOGONALITY IN THE GEOMETRY OF L^p-SPACES
VALUE-DISTRIBUTION OF NON-BLOCH FUNCTIONS
BOUNDARY DISTANCE FUNCTIONS AND q-CONVEXITY OF LOCALLY q-CONVEX DOMAINS WITH CORNERS IN KÄHLER MANIFOLDS
RADIAL IMAGE BY A HOLOMORPHIC FUNCTION ON THE UNIT DISK
BOUNDED AND INTEGRABLE QUADRATIC DIFFERENTIALS: HYPERBOLIC AND EXTREMAL LENGTHS ON RIEMANN SURFACES
SCALING AND HOLOMORPHIC PROJECTIONS ON CONVEX DOMAINS
A BOGOMOLOV-TYPE SMOOTHNESS ON DEFORMATIONS OF QUASI-GORENSTEIN CONE SINGULARITIES OF DIM ≥ 4
ON THE -COHOMOLOGY GROUPS OF STRONGLY q-CONCAVE MANIFOLDS
HOLOMORPHIC FOLIATIONS WITH COMPATIBLE DEGENERATE KÄHLER METRICS: APPLICATIONS TO THE SHAFAREVICH CONJECTURE AND TO FIBRATION THEOREMS
REPRESENTATIONS OF THE THIRD BRAID GROUP AND FENCHEL'S PROBLEM
ON NEVANLINNA'S SECOND MAIN THEOREM
APPLICATIONS OF L² ESTIMATES AND SOME COMPLEX GEOMETRY
ON TOTALLY REAL SETS
INTEGRAL REPRESENTATIONS FOR IN CR MANIFOLDS
THE SECOND MAIN THEOREM FOR LOG CANONICAL R-DIVISORS
HOLOMORPHIC EQUIVALENCE PROBLEM FOR TWO-DIMENSIONAL TUBE DOMAINS WITH POLYNOMIAL INFINITESIMAL AUTOMORPHISMS
ON PSEUDOCONVEX NEIGHBORHOODS OF REAL SUBSPACES
THE FUJITA CONJECTURE AND THE EXTENSION THEOREM OF OHSAWA-TAKEGOSHI
FROM THE BIG PICARD THEOREM TO A FINITENESS THEOREM IN HYPERBOLIC GEOMETRY
REMARKS ON THE HOLOMORPHIC CONVEXITY OF THE UNIVERSAL COVERING SPACE OF A PROJECTIVE MANIFOLD
A DEGENERATION OF LERAY SPECTRAL SEQUENCE BY PROPER KÄHLER MORPHISMS
ON A PROBLEM OF OHSAWA
NORMALITY CRITERIONS FOR FAMILIES OF HOLOMORPHIC MAPPINGS INTO P^N(C)
JULIA SETS FOR COMPLEX DYNAMICS ON PROJECTIVE SPACES
YANG-MILLS CONNECTIONS AND DEFORMATION THEORY OVER COMPACT STRONGLY PSEUDOCONVEX CR MANIFOLDS
ON -MORPHISMS OF COMPLEX SPACES
COMPLEX PARALLELIZABLE MANIFOLDS
ON THE SPECTRAL ZETA FUNCTIONS OF KÄHLER VARIETIES WITH CONICAL SINGULARITIES
ON EXOTIC ALGEBRAIC STRUCTURES ON AFFINE SPACES