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Mapping problems in complex analysis and the $\overline \partial$-problem


Author: S. Bell
Journal: Bull. Amer. Math. Soc. 22 (1990), 233-259
MSC (1985): Primary 30C35, 32H99, 35N15
DOI: https://doi.org/10.1090/S0273-0979-1990-15879-3
MathSciNet review: 1040388
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  • 1. H. Alexander, Proper holomorphic mappings inCn, Indiana Math. J. 26 (1977), 137-146. MR 422699
  • 2. M. S. Baouendi, H. Jacobowitz, and F. Treves, On the analyticity of CR mappings, Ann. of Math. (2) 122 (1985), 365-400. MR 808223
  • 3. M. S. Baouendi and L. P. Rothschild, Germs of CR maps between real analytic hypersurfaces, Invent. Math. 93 (1988), 481-500. MR 952280
  • 4. D. Barrett, Irregularity of the Bergman projection on a smooth bounded domain inCn, Ann. of Math. (2) 119 (1984), 431-436. MR 740899
  • 5. E. Bedford, Proper holomorphic mappings, Bull. Amer. Math. Soc. (N.S.) 10(1984), 157-175. MR 733691
  • 6. S. Bell, Biholomorphic mappings and the $\bar \partial $-problem, Ann. of Math. (2) 114 (1981), 103-113. MR 625347
  • 7. S. Bell, Analytic hypoellipticity of the $\bar \partial $-Neumann problem and extendability of holomorphic mappings, Acta Math. 147 (1981), 109-116. MR 631091
  • 8. S. Bell and D. Catlin, Boundary regularity of proper holomorphic mappings, Duke Math. J. 49 (1982), 385-396. MR 659947
  • 9. S. Bell and S. Krantz, Smoothness to the boundary of conformal maps, Rocky Mountain J. Math. 17 (1987), 23-40. MR 882882
  • 10. S. Bell and E. Ligocka, A simplification and extension of Fefferman's theorem on biholomorphic mappings, Invent. Math. 57 (1980), 283-289. MR 568937
  • 11. S. Bergman, The kernel function and conformal mapping, Math. Surveys no. 5, Amer. Math. Soc. Providence, R. I., 1970. MR 507701
  • 12. D. Catlin, Necessary conditions for subellipticity of the $\bar \partial $-Neumann problem, Ann. of Math. (2) 117 (1983), 147-171. MR 683805
  • 13. D. Catlin, Boundary invariants of pseudoconvex domains, Ann. of Math. (2) 120 (1984), 529-586. MR 769163
  • 14. D. Catlin, Subelliptic estimates for the $øverline\partial$-Neumann problem on pseudoconvex domains, Ann. of Math. (2) 126 (1987), 131-191. MR 898054
  • 15. S. Chern and J. Moser, Real analytic hypersurfaces in complex manifolds, Acta Math. 133 (1974), 219-271. MR 425155
  • 16. J. D'Angelo, Real hypersurfaces, orders of contact, and applications, Ann. of Math. (2) 115 (1982), 615-637. MR 657241
  • 17. K. Diederich and J. E. Fornaess, Pseudoconvex domains: Bounded strictly plurisubharmonic exhaustion functions, Invent. Math. 39 (1977), 129-141. MR 437806
  • 18. K. Diederich and J. E. Fornaess, Boundary regularity of proper holomorphic mappings, Invent. Math. 67 (1982), 363-384. MR 664111
  • 19. K. Diederich and J. E. Fornaess, Proper holomorphic mappings between real-analytic pseudoconvex domains inCn, Math. Ann. 282 (1988), 681-700. MR 970228
  • 20. C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-65. MR 350069
  • 21. B. Fridman, An approximate Riemann mapping theorem in C, Math. Ann. 257(1986), 49-55. MR 849053
  • 22. R. Greene and S. Krantz, Biholomorphic self maps of domains, Lecture Notes in Math., vol. 1276, Springer-Verlag, Berlin and New York, 1987, pp. 136-207. MR 922321
  • 23. L. Hörmander, An introduction to complex analysis in several variables, North-Holland, Amsterdam, 1973. MR 344507
  • 24. N. Kerzman, A Monge-Ampère equation in complex analysis, Proc. Sympos. Pure Math., vol. 30, Amer. Math. Soc. Providence, R.I., 1977, pp. 161-167. MR 454082
  • 25. J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, Ann. of Math. (2) 78 (1963), 112-148. MR 153030
  • 26. J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. II, Ann. of Math. (2) 79 (1964), 450-472. MR 208200
  • 27. J. J. Kohn, A survey of the $\bar \partial $-Neumann problem, Proc. Sympos. Pure Math., vol. 41, Amer. Math. Soc. Providence, R.I., 1984, pp. 137-145. MR 740877
  • 28. S. Krantz, Function theory of several complex variables, Wiley-Interscience, New York, 1982. MR 635928
  • 29. H. Lewy, On the boundary behavior of holomorphic mappings, Acad. Naz. Lincei 35 (1977), 1-8.
  • 30. R. Narasimhan, Several complex variables, Chicago Lectures in Math., Chicago, III.-London, 1971. MR 342725
  • 31. Z. Nehari, Conformal mapping, Dover, New York, 1952. MR 45823
  • 32. L. Nirenberg, S. Webster, and P. Yang, Local boundary regularity of holomorphic mappings, Comm. Pure Appl. Math. 33 (1980), 306-338. MR 562738
  • 33. P. Painlevé, Sur les lignes singulières des functions analytiques, Thèse, Gauthier-Villars, Paris, 1887.
  • 34. S. Pinčuk, On proper holomorphic mappings of strictly pseudoconvex domains, Siberian Math. J. 15 (1974), 909-917. MR 355109
  • 35. S. Pinčuk, On the analytic continuation of holomorphic mappings, Math. USSR-Sb. 27 (1975), 375-392. MR 393562
  • 36. R. M. Range, Holomorphic functions and integral representations in several complex variables, Springer-Verlag, Berlin and New York, 1986. MR 847923
  • 37. J.-P. Rosay, Sur une caractérisation de la boule parmi les domains deCn par son groupe d'automorphismes, Ann. Inst. Fourier (Grenoble) 29 (1979), 91-97. MR 558590
  • 38. J.-P. Rosay, Injective holomorphic mappings, Amer. Math. Monthly 89 (1982), 587-588. MR 674524
  • 39. W. Rudin, Function theory in the unit ball ofCn, Springer-Verlag, Berlin and New York, 1980. MR 601594
  • 40. W. Rudin, Function theory in polydiscs, Benjamin, New York, 1969. MR 255841
  • 41. E. M. Stein, Boundary behavior of holomorphic functions of several complex variables, Math. Notes, no. 1, Princeton Univ. Press, Princeton, N.J., 1972. MR 473215
  • 42. S. Webster, Biholomorphic mappings and the Bergman kernel off the diagonal, Invent. Math. 51 (1979), 155-169. MR 528021
  • 43. S. Webster, On the reflection principle in several complex variables, Proc. Amer. Math. Soc. 71 (1978), 26-28. MR 477138
  • 44. B. Wong, Characterization of the ball in C, Invent. Math. 41 (1977), 253-257. MR 492401

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DOI: https://doi.org/10.1090/S0273-0979-1990-15879-3

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