Modern Methods in Complex Analysis

by Bloom, Thomas; Catlin, David; D'Angelo, John P.; Siu, Yum-Tong; Gunning, Robert C.; Kohn, J. J.

• ISBN13: 9780691044293
• ISBN10: 0691044295
• Format: Hardcover
• Copyright: 1996-02-01
• Publisher: Princeton Univ Pr

Summary

The fifteen articles composing this volume focus on recent developments in complex analysis. Written by well- known researchers in complex analysis and related fields, they cover a wide spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. The topics include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, the Abel-Radon transforms, the action of the Ricci curvature operator, locally symmetric manifolds, the maximum principle, very ampleness criterion, integrability of elliptic systems, and contact geometry. Among the contributions are survey articles, which are especially suitable for readers looking for a comprehensive, well- presented introduction to the most recent important developments in the field. The contributors are R. Bott, M. Christ, J. P. D'Angelo, P. Eyssidieux, C. Fefferman, J. E. Fornaess, H. Grauert, R. S. Hamilton, G. M. Henkin, N. Mok, A. M. Nadel, L. Nirenberg, N. Sibony, Y.-T. Siu, F. Treves, and S. M. Webster.

Table of Contents

Preface
List of Participants
Program of the Conference
The Scientific Work of Robert C. Gunning	p. 3
The Scientific Work of Joseph J. Kohn	p. 16
On Invariants of Manifolds	p. 29
Remarks on Analytic Hypoellipticity of [actual symbol not reproducible]	p. 41
Finite Type Conditions and Subelliptic Estimates	p. 63
Characterization of Certain Holomorphic Geodesic Cycles on Hermitian Locally Symmetric Manifolds of the Noncompact Type	p. 79
On Kohn's Microlocalization of [actual symbol not reproducible] Problems	p. 119
Complex Dynamics in Higher Dimension. II	p. 135
Set Theoretical Real Analytic Spaces	p. 183
An Isoperimetric Estimate for the Ricci Flow on the Two-Sphere	p. 191
Isoperimetric Estimates for the Curve Shrinking Flow in the Plane	p. 201
The Abel-Radon Transform and Several Complex Variables	p. 223
On the Absence of Periodic Points for the Ricci Curvature Operator Acting on the Space of Kahler Metrics	p. 277
The Maximum Principle and Related Topics	p. 283
Very Ampleness Criterion of Double Adjoints of Ample Line Bundles	p. 291
Integrability of Elliptic Overdetermined Systems of Nonlinear First-Order Complex PDE	p. 319
The Holomorphic Contact Geometry of a Real Hypersurface	p. 327
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