Mathematische Annalen

, Volume 292, Issue 1, pp 163–180 | Cite as

Mappings of quadric Cauchy-Riemann manifolds

  • Franc Forstnerič
Article

Mathematics Subject Classification (1991)

32H35 32H40 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Al]
    Alexander, H.: Holomorphic mappings from the ball and polydisc. Math. Ann.209, 249–256 (1974)Google Scholar
  2. [BBR]
    Baouendi, M.S., Bell, S., Rothschild, L.P.: Mappings of three-dimensional CR manifolds and their holomorphic extension. Duke Math. J.56, 503–530 (1988)Google Scholar
  3. [BCT]
    Baouendi, M.S., Chang, C.H., Treves, F.: Microlocal hypo-ellipticity and extension of CR functions. J. Differ. Geom.18, 331–391 (1983)Google Scholar
  4. [BJT]
    Baouendi, M.S., Jacobowitz, H., Treves, F.: On the analyticity of CR mappings. Ann. Math.122, 365–400 (1985)Google Scholar
  5. [BR1]
    Baouendi, M.S., Rothschild, L.P.: Germs of CR maps between analytic real hypersurfaces. Invent. Math.93, 481–500 (1988)Google Scholar
  6. [BR2]
    Baouendi, M.S., Rothschild, L.P.: A general reflection principle inC 2. (Preprint 1989)Google Scholar
  7. [BR3]
    Baouendi, M.S., Rothschild, L.P.: Normal forms for generic manifolds and holomorphic extension of CR functions. J. Differ. Geom.25, 431–467 (1987)Google Scholar
  8. [BT]
    Baouendi, S., Treves, F.: A property of the functions and distributions annihilated by a locally integrable system of complex vectorfields. Ann. Math.113, 387–421 (1981)Google Scholar
  9. [BP]
    Boggess, A., Polking, J.C.: Holomorphic extension of CR functions. Duke Math. J.49, 757–784 (1982)Google Scholar
  10. [BM]
    Bochner, S., Martin, W.T.: Several complex variables. Princeton: Princeton University Press 1948Google Scholar
  11. [CM]
    Chern, S.S., Moser, J.K.: Real hypersurfaces in complex manifolds. Acta Math.133, 219–271 (1975)Google Scholar
  12. [CS]
    Cima, J., Suffridge, T.J.: A reflection principle with applications to proper holomorphic mappings. Math. Ann.265, 489–500 (1983)Google Scholar
  13. [Co1]
    Coupet, B.: Construction de disques analytiques et applications. C.R. Acad. Sci., Paris, Sér. I304 (no. 14), 427–430 (1987)Google Scholar
  14. [Co2]
    Coupet, B.: Régularité d'applications holomorphes sur des variétés totalement réelles; Structure des espaces de Bergman. Thèse, Universite de Provence, Marseille, 1987Google Scholar
  15. [DA1]
    D'Angelo, J.: Proper holomorphic maps between balls of different dimensions. Mich. Math. J.35, 83–90 (1988)Google Scholar
  16. [DA2]
    D'Angelo, J.: Polynomial proper maps between balls. Duke Math. J.57, 211–219 (1988)Google Scholar
  17. [DA3]
    D'Angelo, J.: The structure of proper rational holomorphic maps between balls. (Preprint 1988)Google Scholar
  18. [DF1]
    Diederich, K., Fornæss, J.E.: Proper holomorphic mappings between real-analytic pseudoconvex domains inC n. Math. Ann.282, 681–700 (1988)Google Scholar
  19. [DF2]
    Diederich, K., Fornæss, J.E.: Applications holomorphes propres entre domaines à bord analytique réel. C.R. Acad. Sci. Paris, Sér. I307, 321–324 (1988)Google Scholar
  20. [DW]
    Diederich, K., Webster, S.: A reflection principles for degenerate real hypersurfaces. Duke Math. J.47, 835–843 (1980)Google Scholar
  21. [Dor]
    Dor, A.: Proper holomorphic maps from strongly pseudoconvex domains inC 2 to the unit ball inC 3 and boundary interpolation by proper holomorphic maps. (Preprint 1987)Google Scholar
  22. [For]
    Forstnerič, F.: Extending proper holomorphic mappings of positive codimension. Invent. Math.95, 31–62 (1989)Google Scholar
  23. [Ha]
    Hakim, M.: Applications holomorphes propres continues de domaines strictement pseudoconvexes deC n dans la boule unitéC n+1. (Preprint 1987)Google Scholar
  24. [HN]
    Henkin, G.M., Novikov, R.: Proper mappings of classical domains. In: Linear and complex analysis problem book, pp. 625–627. Berlin Heidelberg New York: Springer 1984Google Scholar
  25. [Le]
    Lewy, H.: On the boundary behavior of holomorphic mappings. Atti Accad. Naz. Lincei35, 1–8 (1977)Google Scholar
  26. [Na]
    Naruki, I.: Holomorphic extension problem for standard real submanifolds of second level. Publ. Res. Inst. Math. Sci.6, 113–187 (1970)Google Scholar
  27. [PS]
    Piatetsky-Shapiro, I.I.: Géometrie des domaines classiques et théorie des fonctions automorphes. Paris: Dunod 1966Google Scholar
  28. [Pin]
    Pinčuk, S.I.: On the analytic continuation of biholomorphic mappings (in Russian). Mat. Sb.98 (18), 416–435 (1975); English transl. in Math. USSR, Sb.27, 375–392 (1975)Google Scholar
  29. [PH]
    Pinčuk, S.I., Hasanov, S.V.: Asymptotically holomorphic functions (in Russian). Mat. Sb.134 (176), 546–555 (1987)Google Scholar
  30. [PT]
    Pinčuk, S.I., Tsyganov, Sh.I.: Smoothness of CR mappings of strongly pseudoconvex hypersurfaces (in Russian). Izv. Akad. Nauk SSSR53, 1120–1129 (1989)Google Scholar
  31. [Ru]
    Rudin, W.: Function theory on the unit ball ofC n. New York: Springer 1980Google Scholar
  32. [Sad]
    Sadullaev, A.: A boundary uniqueness theorem inC n (in Russian). Mat. Sb.101, 501–514 (1976)Google Scholar
  33. [Seg]
    Segre, B.: Intorno al problem di Poincaré della representazione pseudo-conform. Rend. Atti Accad. Naz. Lincei, VI. Ser.13, 676–683 (1931)Google Scholar
  34. [Tu1]
    Tumanov, A.E.: Extending CR functions to a wedge from manifolds of finite type (in Russian). Mat. Sb.136 (178), 128–139 (1988)Google Scholar
  35. [Tu2]
    Tumanov, A.E.: Finite dimensionality of the group of C-R automorphisms of standard C-R manifolds and proper holomorphic mappings of Siegel domains (in Russian) Izv. Akad. Nauk SSSR52, 651–659 (1988)Google Scholar
  36. [TH1]
    Tumanov, A.E., Henkin, G.M.: Local characterization of holomorphic automorphisms of Siegel domains (in Russian) Funkts. Anal.17, 49–61 (1983)Google Scholar
  37. [TH2]
    Tumanov, A.E., Henkin, G.M.: Local characterization of holomorphic automorphisms of classical domains (in Russian). Dokl. Akad. Nauk SSSR267, 796–799 (1982)Google Scholar
  38. [We1]
    Webster, S.M.: On the mapping problem for algebraic real hypersurfaces. Invent. Math.43, 53–68 (1977)Google Scholar
  39. [We2]
    Webster, S.M.: Holomorphic mappings of domains with generic corners. Proc. Am. Math. Soc.86, 236–240 (1982)Google Scholar
  40. [We3]
    Webster, S.M.: Analytic discs and the regularity of C-R mappings of real submanifolds inC n Proc. Symp. Pure Math.41, 199–208 (1984)Google Scholar

Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Franc Forstnerič
    • 1
  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA

Personalised recommendations