Several Complex Variables

✍ Scribed by Fornaess J.E. (ed.)

• Publisher: PUP
• Year: 1992
• Tongue: English
• Leaves: 707
• Category: Library

✦ Synopsis

There was a special year devoted to the topic of several complex variables at the Mittag-Leffler Institute in Stockholm, Sweden, and this volume contains the resulting survey papers and research papers. The work covers a broad spectrum of developments in this field. The contributors include H. Alexander; F. Almgren; E. Almar; M. Andersson; E. Bedford; J. Belanger; S. Bell; B. Berndtsson; U. Cegrell; C.H. Chang and H.P. Lee; J. Chaumat and A.M. Chollet; J. D'Angelo; J. P. Demailley; P. Dolbeault; A. Dor; F. Forstneric; B. Gaveau, M. Okada, and T. Okada; R. Greene and S. Krantz; A. Iordan; C. Laurent-Thiebaut and J. Leiterer; L. Lempert; I. Lieb and M. Range; L. Qi-King; P. Manne; A. Noell; M. Passare; J. Riihentaus; J. P. Rosay and W. Rudin; R. Saerens and W. Zame; A. Sergeev; N. Sibony; E.L. Stout; F. Treves; S. Webster; H. H. Wu; and A. Zeriahi.

✦ Table of Contents

Table of Contents......Page v
Introduction......Page vii
1. Removable Sets for CR Functions......Page 1
2. Geometric Measure Theory......Page 8
3. \bar{\partial}_t-Equation and Nonfactorization......Page 22
4. L^p Estimates for the \bar{\partial}-Equation......Page 34
5. Survey of Pluri-Potential Theory......Page 48
6. Holder Estimates for \bar{\partial} in C^2......Page 98
7. Algebraic Mappings......Page 126
8. Levi-Flat Surfaces with Circular Sections......Page 136
9. Weighted Integral Formulas......Page 160
10. Peak Sets and Representing Measures......Page 188
11. Explicit Solutions......Page 194
12. Noyaux pour résoudre l'équation \bar{\partial}......Page 205
13. Proper Rational Holomorphic Maps......Page 227
14. Holomorphic Morse Inequalities......Page 245
15. On the Structure of Residual Currents......Page 258
16. Properties of Smooth Proper Holomorphic Maps......Page 274
17. Proper Holomorphic Mappings: A Survey......Page 297
18. Explicit Heat Kernels......Page 364
19. Techniques for Studying Automorphisms......Page 389
20. Peak Sets in Domains......Page 411
21. The Andreotti-Vesentini Separation Theorem......Page 416
22. Elliptic and Hyperbolic Tubes......Page 440
23. A Survey of the \bar{\partial}-Problem......Page 457
24. The \bar{\partial}-Neumann Kernel......Page 473
25. The Heat Kernel......Page 483
26. Removable Singularities for \bar{\partial}_b......Page 507
27. Carleman Approximation......Page 519
28. Peak Functions for Pseudoconvex Domains......Page 529
29. Support of Residue Currents......Page 542
30. Nullsets for BMO Functions......Page 550
31. Holomorphic Embeddings......Page 563
32. Local Automorphism Group......Page 570
33. On Matrix Reinhardt and Circled Domains......Page 573
34. On Holder Estimates for \bar{\partial}......Page 587
35. Removable Singularities......Page 600
36. An Implicit Function Theorem......Page 630
37. Old and New Invariant Metrics......Page 640
38. Inégalités de Markov et Développement......Page 683