Skip to main content
SpringerLink
Log in

The dirichlet problem for a complex Monge-Ampère equation

  • Published:
Inventiones mathematicae Aims and scope

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. Alexandrov, A. D.: The Dirichlet problem for the equation Det ∥z i,j ∥=ψ(z 1,...,z n ,x 1,...,x n ), I. Vestnik, Leningrad Univ.13, No. 1, 5–24 (1958)

    Google Scholar 

  2. Bergman, S.: Functions of extended class in the theory of functions of several complex variables. Trans. Amer. Math. Soc.63, 523–547 (1948)

    Google Scholar 

  3. Bergman, S.: Kernel functions and extended classes in the theory of functions of complex variables, Colloque sur les fonctions de plusieur variables. Bruxelles pp. 135–157 (1953)

  4. Bremermann, H.: On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Characterization of Silov boundaries. Trans. Amer. Math. Soc.91, 246–276 (1959)

    Google Scholar 

  5. Cheng, S.-Y., Yau, S.-T.: Complete affine hypersurfaces, Parts I, II, III. To appear

  6. Chern, S. S., Levine, Harold I., Nirenberg, L.: Intrinsic norms on a complex manifold. Global Analysis (Papers in honor of K. Kodaira), pp. 119–139 Tokyo: Univ. of Tokyo Press 1969

    Google Scholar 

  7. Chern, S. S., Moser, J.: Real hypersurfaces in complex manifolds. Acta Math.133, 219–271 (1974)

    Google Scholar 

  8. Christoffers, H.: Princeton University Thesis, to appear

  9. Diederich, K.: Über die 1. und 2. Ableitungen der Bergmannschen Kernfunktion und ihr Randverhalten. Math. Ann.203, 129–170 (1963)

    Article  Google Scholar 

  10. Fefferman, C.: Monge-Ampere equations, the Bergman Kernel, and geometry of pseudoconvex domains. Ann. of Math.,103, 395–416 (1976)

    Google Scholar 

  11. Gluck, H.: Manifolds with preassigned curvature—a survey. Bull. Amer. Math. Soc.81, 313–329 (1975)

    Google Scholar 

  12. Goffman, C., Serrin, J.: Sublinear functions of measures and variational integrals. Duke Math. J.31, 159–178 (1964)

    Article  Google Scholar 

  13. Hörmander, L.: Complex analysis in several variables. New York: North Holland/American Elsevier 1973

    Google Scholar 

  14. Hörmander, L.:L 2 estimates and existence theorems for the ζ operator. Acta Math.113, 89–152 (1965)

    Google Scholar 

  15. Kerzman, N., Kohn, J.J., Nirenberg, L.: Lecture at Amer. Math. Soc. Conference on Several Complex Variables. Williamstown, Mass, August, 1975

  16. Koppelman, W.: The Cauchy integral formula for functions of several complex variables, Bull. Amer. Math. Soc.73, 373–377 (1967)

    Google Scholar 

  17. Lelong, P.: Plurisubharmonic functions and positive differential forms, New York: Gordon and Breach 1969

    Google Scholar 

  18. Pelles, D. A.: Intrinsic measures on complex manifolds and holomorphic mappings. Amer. Math. Soc. Memoir Number96, 1970

  19. Pogorelov, A. V.: Monge-Ampere equations of elliptic type. Groningen: Noordhoff 1964

    Google Scholar 

  20. Pogorelov, A. V.: The Dirichlet problem for then-dimensional analogue of the Monge-Ampere equation, Soviet Math. Dokl.12, 1727–1731 (1971)

    Google Scholar 

  21. Rudin, W.: Real and complex analysis. New York: McGraw Hill 1974

    Google Scholar 

  22. Siu, Y. T.: Extension of meromorphic maps. Ann. of Math.102, 421–462 (1975)

    Google Scholar 

  23. Walsh, J. B.: Continuity of envelopes of plurisubharmonic functions. J. Math. Mech.18, 143–148 (1968)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Courant Institute of Mathematical Sciences, 251 Mercer, 10012, New York, NY, USA

    Eric Bedford

  2. Department of Mathematics, University of Michigan, 48104, Ann Arbor, MI, USA

    B. A. Taylor

Authors
  1. Eric Bedford
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. B. A. Taylor
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by a Sloan Foundation Grant to Courant Institute of Mathematical Sciences, New York University and the Army Research Office grant number DAHCO4-75-G-0149

Research supported in part by the National Science Foundation grant number GP37628

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bedford, E., Taylor, B.A. The dirichlet problem for a complex Monge-Ampère equation. Invent Math 37, 1–44 (1976). https://doi.org/10.1007/BF01418826

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01418826

Keywords

Search

Navigation