Analysis and Geometry in Several Complex Variables

1. Front Matter

   Pages i-xi

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2. The Bergman Kernel and a Theorem of Tian

   • David Catlin

   Pages 1-23

3. Some Involutive Structures in Analysis and Geometry

   • Michael Eastwood

   Pages 25-38

4. The Bergman Kernel in Quantum Mechanics

   • Charles L. Fefferman

   Pages 39-58

5. WKB and the Periodic Table

   • Charles L. Fefferman

   Pages 59-62

6. Local Sobolev—Bergman Kernels of Strictly Pseudoconvex Domains

   • Kengo Hirachi, Gen Komatsu

   Pages 63-96

7. Quantitative Estimates for Global Regularity

   • J. J. Kohn

   Pages 97-128

8. Pdes Associated to the CR Embedding Theorem

   • Masatake Kuranishi

   Pages 129-157

9. \( \bar{\partial } \) and \( {\bar{\partial }_b} \) Problems on Nonsmooth Domains

   • Joachim Michel, Mei-Chi Shaw

   Pages 159-192

10. A Note on the Closed Rangeness of Vector Bundle Valued Tangential Cauchy—Riemann Operator

    • Kimio Miyajima

    Pages 193-208

11. Discrete Groups of Complex Hyperbolic Isometries and Pseudo-Hermitian Structures

    • Shin Nayatani

    Pages 209-237

12. Pseudoconvex Domains in ℙⁿ: A Question on the 1-Convex Boundary Points

    • Takeo Ohsawa

    Pages 239-252

13. Existence and Applications of Analytic Zariski Decompositions

    • Hajime Tsuji

    Pages 253-271

14. Segre Polar Correspondence and Double Valued Reflection for General Ellipsoids

    • S. M. Webster

    Pages 273-288

15. G2-Geometry of Overdetermined Systems of Second Order

    • Keizo Yamaguchi

    Pages 289-314

16. Back Matter

    Pages 315-315

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This volume consists of a collection of articles for the proceedings of the 40th Taniguchi Symposium Analysis and Geometry in Several Complex Variables held in Katata, Japan, on June 23-28, 1997. Since the inhomogeneous Cauchy-Riemann equation was introduced in the study of Complex Analysis of Several Variables, there has been strong interaction between Complex Analysis and Real Analysis, in particular, the theory of Partial Differential Equations. Problems in Complex Anal­ ysis stimulate the development of the PDE theory which subsequently can be applied to Complex Analysis. This interaction involves Differen­ tial Geometry, for instance, via the CR structure modeled on the induced structure on the boundary of a complex manifold. Such structures are naturally related to the PDE theory. Differential Geometric formalisms are efficiently used in settling problems in Complex Analysis and the results enrich the theory of Differential Geometry. This volume focuses on the most recent developments in this inter­ action, including links with other fields such as Algebraic Geometry and Theoretical Physics. Written by participants in the Symposium, this vol­ ume treats various aspects of CR geometry and the Bergman kernel/ pro­ jection, together with other major subjects in modern Complex Analysis. We hope that this volume will serve as a resource for all who are interested in the new trends in this area. We would like to express our gratitude to the Taniguchi Foundation for generous financial support and hospitality. We would also like to thank Professor Kiyosi Ito who coordinated the organization of the symposium.

• CR manifold
• Complex analysis
• Complex variables
• Pseudoconvexity
• algebra
• differential geometry
• manifold
• vector bundle

• Department of Mathematics, Osaka University, Toyonaka, Osaka, Japan

  Gen Komatsu

• Department of Mathematics, Columbia University, New York, USA

  Masatake Kuranishi

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