On three-dimensional Cauchy-Riemann manifolds
HTML articles powered by AMS MathViewer
- by László Lempert PDF
- J. Amer. Math. Soc. 5 (1992), 923-969 Request permission
References
- M. S. Baouendi, Linda Preiss Rothschild, and F. Trèves, CR structures with group action and extendability of CR functions, Invent. Math. 82 (1985), no. 2, 359–396. MR 809720, DOI 10.1007/BF01388808
- David E. Barrett, A remark on the global embedding problem for three-dimensional CR manifolds, Proc. Amer. Math. Soc. 102 (1988), no. 4, 888–892. MR 934861, DOI 10.1090/S0002-9939-1988-0934861-9
- Eric Bedford and B. A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation, Invent. Math. 37 (1976), no. 1, 1–44. MR 445006, DOI 10.1007/BF01418826
- J. Bland and T. Duchamp, Moduli for pointed convex domains, Invent. Math. 104 (1991), no. 1, 61–112. MR 1094047, DOI 10.1007/BF01245067
- L. Boutet de Monvel, Intégration des équations de Cauchy-Riemann induites formelles, Séminaire Goulaouic-Lions-Schwartz 1974–1975; Équations aux derivées partielles linéaires et non linéaires, Exp. No. 9, Centre Math., École Polytech., Paris, 1975, pp. 14 (French). MR 0409893
- Daniel M. Burns Jr., Global behavior of some tangential Cauchy-Riemann equations, Partial differential equations and geometry (Proc. Conf., Park City, Utah, 1977) Lecture Notes in Pure and Appl. Math., vol. 48, Dekker, New York, 1979, pp. 51–56. MR 535588
- Daniel M. Burns and Charles L. Epstein, Embeddability for three-dimensional CR-manifolds, J. Amer. Math. Soc. 3 (1990), no. 4, 809–841. MR 1071115, DOI 10.1090/S0894-0347-1990-1071115-4
- Henri Cartan, Quotient d’un espace analytique par un groupe d’automorphismes, Algebraic geometry and topology. A symposium in honor of S. Lefschetz, Princeton University Press, Princeton, N.J., 1957, pp. 90–102 (French). MR 0084174 Y. Cheng and J. Lee, personal communication.
- G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI 10.1002/cpa.3160270403
- Hans Grauert, Über Modifikationen und exzeptionelle analytische Mengen, Math. Ann. 146 (1962), 331–368 (German). MR 137127, DOI 10.1007/BF01441136
- F. Reese Harvey and H. Blaine Lawson Jr., On boundaries of complex analytic varieties. II, Ann. of Math. (2) 106 (1977), no. 2, 213–238. MR 499285, DOI 10.2307/1971093
- Howard Jacobowitz and François Trèves, Nonrealizable CR structures, Invent. Math. 66 (1982), no. 2, 231–249. MR 656622, DOI 10.1007/BF01389393
- Garo K. Kiremidjian, A direct extension method for CR structures, Math. Ann. 242 (1979), no. 1, 1–19. MR 537322, DOI 10.1007/BF01420478
- Shoshichi Kobayashi, Hyperbolic manifolds and holomorphic mappings, Pure and Applied Mathematics, vol. 2, Marcel Dekker, Inc., New York, 1970. MR 0277770
- Kunihiko Kodaira, Complex manifolds and deformation of complex structures, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 283, Springer-Verlag, New York, 1986. Translated from the Japanese by Kazuo Akao; With an appendix by Daisuke Fujiwara. MR 815922, DOI 10.1007/978-1-4613-8590-5
- J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. I, Ann. of Math. (2) 78 (1963), 112–148. MR 153030, DOI 10.2307/1970506
- J. J. Kohn, The range of the tangential Cauchy-Riemann operator, Duke Math. J. 53 (1986), no. 2, 525–545. MR 850548, DOI 10.1215/S0012-7094-86-05330-5
- A. Korányi and H. M. Reimann, Quasiconformal mappings on the Heisenberg group, Invent. Math. 80 (1985), no. 2, 309–338. MR 788413, DOI 10.1007/BF01388609
- Adam Korányi and Hans Martin Reimann, Quasiconformal mappings on CR manifolds, Complex geometry and analysis (Pisa, 1988) Lecture Notes in Math., vol. 1422, Springer, Berlin, 1990, pp. 59–75. MR 1055843, DOI 10.1007/BFb0089405
- László Lempert, La métrique de Kobayashi et la représentation des domaines sur la boule, Bull. Soc. Math. France 109 (1981), no. 4, 427–474 (French, with English summary). MR 660145
- László Lempert, Intrinsic distances and holomorphic retracts, Complex analysis and applications ’81 (Varna, 1981) Publ. House Bulgar. Acad. Sci., Sofia, 1984, pp. 341–364. MR 883254
- László Lempert, Solving the degenerate complex Monge-Ampère equation with one concentrated singularity, Math. Ann. 263 (1983), no. 4, 515–532. MR 707246, DOI 10.1007/BF01457058
- László Lempert, Symmetries and other transformations of the complex Monge-Ampère equation, Duke Math. J. 52 (1985), no. 4, 869–885. MR 816389, DOI 10.1215/S0012-7094-85-05245-7
- László Lempert, A precise result on the boundary regularity of biholomorphic mappings, Math. Z. 193 (1986), no. 4, 559–579. MR 867348, DOI 10.1007/BF01160475
- Ewa Ligocka, The Hölder continuity of the Bergman projection and proper holomorphic mappings, Studia Math. 80 (1984), no. 2, 89–107. MR 781328, DOI 10.4064/sm-80-2-89-107
- J. Morrow and H. Rossi, Some general results on equivalence of embeddings, Recent developments in several complex variables (Proc. Conf., Princeton Univ., Princeton, N. J., 1979) Ann. of Math. Stud., vol. 100, Princeton Univ. Press, Princeton, N.J., 1981, pp. 299–325. MR 627765
- Jürgen Moser, On the volume elements on a manifold, Trans. Amer. Math. Soc. 120 (1965), 286–294. MR 182927, DOI 10.1090/S0002-9947-1965-0182927-5
- L. Nirenberg, A certain problem of Hans Lewy, Uspehi Mat. Nauk 29 (1974), no. 2(176), 241–251 (Russian). Translated from the English by Ju. V. Egorov; Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. MR 0492752
- Peter Orlik, Seifert manifolds, Lecture Notes in Mathematics, Vol. 291, Springer-Verlag, Berlin-New York, 1972. MR 0426001
- Giorgio Patrizio, Parabolic exhaustions for strictly convex domains, Manuscripta Math. 47 (1984), no. 1-3, 271–309. MR 744324, DOI 10.1007/BF01174598
- H. Rossi, Attaching analytic spaces to an analytic space along a pseudoconcave boundary, Proc. Conf. Complex Analysis (Minneapolis, 1964) Springer, Berlin, 1965, pp. 242–256. MR 0176106
- H. L. Royden, Remarks on the Kobayashi metric, Several complex variables, II (Proc. Internat. Conf., Univ. Maryland, College Park, Md., 1970) Lecture Notes in Math., Vol. 185, Springer, Berlin, 1971, pp. 125–137. MR 0304694
- Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. MR 0210112
- Noboru Tanaka, A differential geometric study on strongly pseudo-convex manifolds, Lectures in Mathematics, Department of Mathematics, Kyoto University, No. 9, Kinokuniya Book Store Co., Ltd., Tokyo, 1975. MR 0399517
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: J. Amer. Math. Soc. 5 (1992), 923-969
- MSC: Primary 32F40; Secondary 32C16, 32G07
- DOI: https://doi.org/10.1090/S0894-0347-1992-1157290-3
- MathSciNet review: 1157290