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Parabolic exhaustions and analytic coverings

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References

  • [Bau] Baum, P.: Structure of foliation singularities. Adv. Math.15, 361–374 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  • [BauBo] Baum, P., Bott, R.: Singularities of holomorphic foliations, J. Differ. Geom.7, 279–342 (1972)

    MATH  MathSciNet  Google Scholar 

  • [BeBu] Bedford, E., Burns, D.: Holomorphic mappings of annuli in ℂn and the associated extremal function. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.6 (no. 3), 381–414 (1979)

    MATH  MathSciNet  Google Scholar 

  • [BeKa] Bedford, E., Kalka, M.: Foliations and complex Monge-Ampère equations. Commun Pure Appl. Math.30 (no. 5), 543–571 (1977)

    MATH  MathSciNet  Google Scholar 

  • [BeTa] Bedford, E., Taylor, B.A.: The Dirichlet problem for a complex Monge-Ampère equation. Invent. Math.37, 1–44 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  • [Boh] Bohnhorst, G.: Einfache holomorphe Abbildungen. Math. Ann.275 (no. 3), 513–520 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • [Bom] Bombieri, E.: Addendum to my paper: “Algebraic values of meromorphic maps”. Invent. Math.11, 163–166 (1970)

    Article  MathSciNet  Google Scholar 

  • [Bor] Borel, A.: Linear algebraic groups, second ed. (Grad. Texts Math., vol. 126) Berlin Heidelberg New York: Springer 1991

    MATH  Google Scholar 

  • [Bu1] Burns, D.: Curvatures of Monge-Ampère foliations and parabolic manifolds. Ann. Math., II. Ser.115 (no. 2), 349–373 (1982)

    MathSciNet  Google Scholar 

  • [Bu2] Burns, D.: Les équations de Monge-Ampère homogènes, et des exhaustions speciales de variétés affines. In: Goulaouic-Meyer-Schwartz seminar 1983–1984, exp. no. 4. Palaiseau: Ecole Polytech. 1984

    Google Scholar 

  • [Ch] Chirka, E.M.: Complex analytic sets. (Math. Appl., Sov. Ser., vol. 46) Dordrecht Boston: Kluwer 1989

    MATH  Google Scholar 

  • [CoGr] Cornalba, M., Griffiths, P.: Analytic cycles and vector bundles on non-compact algebraic varieties. Invent. Math.28 (no. 1), 1–106 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  • [Del] Deligne, P.: Équations différentielles à points singuliers réguliers. (Lect. Notes Math., vol. 163) Berlin Heidelberg New York: Springer 1970

    MATH  Google Scholar 

  • [Dem] Demailly, J-P.: Mesures de Monge-Ampère et caractérisation géométrique des variétés algébriques affines. Mém. Soc. Math. Fr., Nouv. Sér. no. 19 (1985)

  • [DiFo] Diederich, K., Fornæss, J.E.: Pseudoconvex domains with real-analytic boundary. Ann. Math., II Ser.107 (no. 2), 371–384 (1978)

    Google Scholar 

  • [DuKa1] Duchamp, T., Kalka, M.: Invariants of complex foliations and the Monge-Ampère equation. Mich. Math J.35 (no. 1), 91–115 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  • [DuKa2] Duchamp, T., Kalka, M.: Complex foliations. In: Cheng, S.-Y. et al. (eds.) Recent developments in geometry. Los Angeles 1987. (Contemp. Math., vol. 101, pp. 323–338) Providence, RI.: Am. Math. Soc. 1989

    Google Scholar 

  • [Fo] Foote, R.L.: Homogeneous complex Monge-Ampère equations and algebraic embeddings of parabolic manifolds. Indiana Univ. Math. J.39 (no. 4), 1245–1273 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  • [Gó-M] Gómez-Mont, X.: Foliations by curves of complex analytic spaces. In: Verjovsky, A. (ed.) The Lefschetz centennial conference. Mexico City 1984. (Contemp. Math., vol. 58, part III, pp. 123–141) Providence, RI.: Am. Math. Soc. 1987

    Google Scholar 

  • [GrRe] Grauert, H., Remmert, R.: Komplexe Räume. Math. Ann.136 (no. 3), 245–318 (1958)

    Article  MATH  MathSciNet  Google Scholar 

  • [GrKi] Griffiths, P., King, J.: Nevanlinna theory and holomorphic mappings between algebraic varieties. Acta Math.130 (no. 3–4), 145–220 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  • [Ho1] Holmann, H.: Holomorphe Blätterungen komplexer Räume. Comment. Math. Helv.47 (no. 2), 185–204 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  • [Ho2] Holmann, H.: On the stability of holomorphic foliations with all leaves compact. In: Hervier, Y., Hirschowitz, A. (eds.) Variètès Analytiques Compactes, Colloq., Nice 1977. (Lect. Notes Math., vol. 683, pp. 217–248) Berlin Heidelberg New York: Springer 1978

    Chapter  Google Scholar 

  • [Na] Narasimhan, R.: Several complex variables. (Chicago Lect. Math.) Chicago: The University of Chicago Press 1971

    MATH  Google Scholar 

  • [No] Northcott, D.G.: Affine sets and affine groups. (Lond. Math. Soc. Lect. Note Ser., vol. 39) Cambridge New York: Cambridge University Press 1980

    MATH  Google Scholar 

  • [ReSt] Remmert, R., Stein, K.: Über die wesentlichen Singularitäten analytischer Mengen. Math. Ann.126, 263–306 (1953)

    Article  MATH  MathSciNet  Google Scholar 

  • [Sa] Sadullaev, A.: Plurisubharmonic measures and capacities on complex manifolds. Usp. Mat. Nauk36 (no. 4), 53–105 (1981); English transl. in Russ. Math. Surv.36 (no. 4), 61–119 (1981)

    MATH  MathSciNet  Google Scholar 

  • [Si] Simha, R.R.: On the analyticity of certain singularity sets. J. Indian Math. Soc., New Ser.39, 281–283 (1975)

    MATH  MathSciNet  Google Scholar 

  • [St] Stoll, W.: The characterization of strictly parabolic manifolds. Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser.7 (no. 1), 87–154 (1980)

    MATH  MathSciNet  Google Scholar 

  • [Wo] Wong, P.M.: Geometry of the complex homogeneous Monge-Ampère equation. Invent. Math.67 (no. 2), 261–274 (1982)

    Article  MATH  MathSciNet  Google Scholar 

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Lárusson, F. Parabolic exhaustions and analytic coverings. Math Z 215, 415–435 (1994). https://doi.org/10.1007/BF02571722

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