Andreotti-Grauert theory by integral formulas

Title Page......Page 2
Copyright Page......Page 3
Preface......Page 4
Contents......Page 6
Goto 7 /FitH 555. Generalities about differential forms and currents......Page 8
1. The Martinelli-Boehner-Koppelman formula and the Kodaira finite-ness theorem......Page 20
2. Cauchy-Fantappie formulas, the Poincare dbar-lemma, the Dolbeault isomorphism and smoothing of the dbar-cohomology......Page 33
3. Piecewise Cauchy-Fantappie formulas......Page 45
4. q-convex functions......Page 58
5. q-convex manifolds......Page 64
8. q-concave functions and q-concave manifolds......Page 72
Summary......Page 76
7. Local solution of au=fo r on strictly q-convex domains with r>n-q......Page 77
8. Local approximation of 3-closed (0,n-q-1)-forms on strictly q-convex domains......Page 82
9. Uniform estimates for the local solutions of the a-equation constructed in Sect. 7......Page 85
10. Local uniform approximation of a-closed (0,n-q-l)-forms on strictly q-convex domains......Page 92
11. Finiteness of the Dolbeault oohomology of order r with uniform estimates on strictly q-convex domains with r>n-q......Page 95
12. Global uniform approximation of a-closed (0,n-q-1)-forms......Page 99
Summary......Page 116
13. Local solution of & =fO r on strictly q-concave domains with 114. Uniform estimates for the local solutions of the a-equation obtained in Sect. 13......Page 127
15. Invariance of the Dolbeault cohomology of order O16. A uniqueness theorem for the Dolbeault cohomology of order q with respect to q-concave extensions......Page 143
17. The Martineau theorem on the representation of the Dolbeault cohomology of a concave domain by the space of holomorphic functions on the dual domain......Page 145
18. Solution of the E.Levi problem for the Dolbeault cohomology......Page 155
19. The Andreotti-Vesentini separation theorem for the Dolbeault cohomology of order q on q-concave manifolds......Page 163
20. Solvability criterions for &=f and duality between the Dolbeault cohomology with compact support and the usual Dolbeault cohomology......Page 196
21. The domain Iz0I2+ +Izg12 < Izq+112+ +Iz.I2......Page 209
22. The condition Z(r)......Page 210
23. The Rossi theorem on attaching complex manifolds to a complex manifold along a strictly pseudoconcave boundary of real dimension >5......Page 212
24. Rossi\'s example of a real 3-dimensional boundary which cannot be embedded into strictly pseudoconcave C^N......Page 215
NOTES......Page 219
PROBLEMS......Page 225
APPENDIX A. Estimation of some integrals (the smooth case)......Page 231
APPENDIX B. Estimation of some integrals (the non-smooth case)......Page 240
BIBLIOGRAPHY......Page 261
LIST OF SYMBOLS......Page 267
SUBJECT INDEX......Page 269