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Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds

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References

  1. Bedford, E.: Survey of pluri-potential theory. Proceedings of the Special Year in Complex Analysis at the Mittag-Leffler Institute. Princeton: Princeton University Press, to appear

  2. Bedford, E., Kalka, M.: Foliations and complex Monge-Ampère equation. Commun. Pure Appl. Math.30, 543–571 (1977)

    Google Scholar 

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

    Google Scholar 

  4. Bremmermann, H.: On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Shilov boundaries. Trans. Am. Math. Soc.91, 246–276 (1956)

    Google Scholar 

  5. Burns, D.: Curvatures of Monge-Ampère foliations and parabolic manifolds. Ann. Math.115, 349–373 (1982)

    Google Scholar 

  6. Eschenburg, J.H., Sullivan, J.: Growth of Jacobi fields and divergence of geodesics. Math. Z.150, 221–237 (1976)

    Google Scholar 

  7. Harvey, R., Wells, R.: Zero sets of nonnegative strictly plurisubharmonic functions. Math. Ann.201, 165–170 (1973)

    Google Scholar 

  8. Klingenberg, W.: Riemannian geometry. Berlin New York: de Gruyter 1982

    Google Scholar 

  9. Koosis, P.: Introduction toH p -spaces. Lond. Math. Soc. Lecture Note Ser. 40. Cambridge: Cambridge University Press 1980

    Google Scholar 

  10. Lempert, L.: Elliptic and hyperbolic tubes. Proceedings of the Special Year in Complex Analysis at the Mittag-Leffler Institute. Princeton: Princeton University Press, to appear

  11. Patrizio, G., Wong, P.M.: Stein manifolds with compact symmetric center. Preprint

  12. Stoll, W.: The characterization of strictly parabolic manifolds. Ann. Scuola. Norm. Sup. Pisa7, 87–154 (1980)

    Google Scholar 

  13. Szőke, R.: Monge-Ampère models. Ph. D. thesis, Notre Dame (1990)

  14. Szöke, R.: Complex structures on the tangent bundle of Riemannian manifolds. Math. Ann. To appear

  15. Wong, P.M.: Geometry of the homogeneous Monge-Ampère equation. Invent. Math.67, 261–274 (1982)

    Article  Google Scholar 

  16. Wolf, J.: Spaces of constant curvature, 5th ed. Wilmington: Publish or Perish 1984

    Google Scholar 

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Research in part supported by an NSF grant

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Lempert, L., Szőke, R. Global solutions of the homogeneous complex Monge-Ampère equation and complex structures on the tangent bundle of Riemannian manifolds. Math. Ann. 290, 689–712 (1991). https://doi.org/10.1007/BF01459268

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