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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.
List of contents
| Preface | |
| List of Participants | |
| Program of the Conference | |
| The Scientific Work of Robert C. Gunning | 3 |
| The Scientific Work of Joseph J. Kohn | 16 |
| On Invariants of Manifolds | 29 |
| Remarks on Analytic Hypoellipticity of [actual symbol not reproducible]< | 41 |
| Finite Type Conditions and Subelliptic Estimates | 63 |
| Characterization of Certain Holomorphic Geodesic Cycles on Hermitian Locally Symmetric Manifolds of the Noncompact Type | 79 |
| On Kohn's Microlocalization of [actual symbol not reproducible] Problems | 119 |
| Complex Dynamics in Higher Dimension. II | 135 |
| Set Theoretical Real Analytic Spaces | 183 |
| An Isoperimetric Estimate for the Ricci Flow on the Two-Sphere | 191 |
| Isoperimetric Estimates for the Curve Shrinking Flow in the Plane | 201 |
| The Abel-Radon Transform and Several Complex Variables | 223 |
| On the Absence of Periodic Points for the Ricci Curvature Operator Acting on the Space of Kahler Metrics | 277 |
| The Maximum Principle and Related Topics | 283 |
| Very Ampleness Criterion of Double Adjoints of Ample Line Bundles | 291 |
| Integrability of Elliptic Overdetermined Systems of Nonlinear First-Order Complex PDE | 319 |
| The Holomorphic Contact Geometry of a Real Hypersurface | 327 |
About the author
Thomas Bloom is Professor of Mathematics at the University of Toronto.
David W. Catlin is Professor of Mathematics at Purdue University.
John P. D'Angelo is Professor of Mathematics at the University of Illinois, Urbana.
Yum-Tong Siu is William Elwood Byerly Professor of Mathematics at Harvard University.
Summary
Includes fifteen articles which focus on the developments in complex analysis. This work covers a spectrum of research using the methods of partial differential equations as well as differential and algebraic geometry. It covers topics that include invariants of manifolds, the complex Neumann problem, complex dynamics, Ricci flows, and more.
