Skip to main content
SpringerLink
Log in

Stability of envelopes of holomorphy and the degenerate Monge-Ampère equation

  • Published:
Mathematische Annalen Aims and scope Submit manuscript

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. Bedford, E.: Extremal plurisubharmonic functions for certain domains in ℂ2. Indiana U. Math. J.28, 613–626 (1979)

    Article  Google Scholar 

  2. Bedford, E.: Example of a plurisubharmonic measure on the unit ball in ℂ2.Michigan Math. J.27 365–370 (1980)

    Article  Google Scholar 

  3. Bedford, E., Burns, D.: Holomorphic mapping of annuli in ℂn and the associated extremal function. Ann. Scuola. Norm. Sup. Pisa6, 381–414 (1979)

    Google Scholar 

  4. Bedford, E., Fornaess, J. E.: Counterexamples to regularity for the complex Monge-Ampère equation. Invent. Math.50, 129–134 (1979)

    Google Scholar 

  5. Bedford, E., Gaveau, B.: Envelopes of holomorphy of certain 2-spheres in ℂ2. Am. J. Math. (to appear)

  6. Bedford, E., Kalka, M.: Foliations and complex Monge-Ampère equations. Comm. Pure Appl. Math.30, 543–571 (1977).

    Google Scholar 

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

    Google Scholar 

  8. Bishop, E.: Differentiable manifolds in complex Euclidean space. Duke Math. J.32, 1–22 (1965)

    Google Scholar 

  9. Bremermann, H.: On a generalized Dirichlet problem for plurisubharmonic functions and pseudoconvex domains. Charaterization of Silov boundaries. Trans. A.M.S.91, 246–276 (1959)

    Google Scholar 

  10. Cafarelli, L., Kinderlehrer, D.: Potential methods in variational inequalities. J. Analyse Math.37, 285–295 (1980)

    Google Scholar 

  11. Docquier, F., Grauert, H.: Levisches Problem und Rungescher Satz für Teilgebiete Steinscher Mannigfaltigkeiten. Math. Ann.140, 94–123 (1960)

    Google Scholar 

  12. Hill, C.D., Taiani, G.: Families of analytic disks in ℂn with boundaries in a prescribed CR submanifold. Ann. Scuola Norm. Sup. Pisa5, (327–380 (1978)

    Google Scholar 

  13. Kinderlehrer, D.: Variational inequalities and free boundary problems.Bull. A.M.S.84, 7–26 (1978)

    Google Scholar 

  14. Moriyón, R.: Regularity for the Dirichlet problem for the complex Monge-Ampère equation det\((u_{j\bar k} ) = 0\). Proc. Nat. Acad. Sci. USA76, 1022–1023 (1979)

    Google Scholar 

  15. Moriyón, R.: Regularity of the Dirichlet problem for the degenerate complex Monge-Ampère equation. Comm. Pure Appl. Math. (to appear)

  16. Schaeffer, D.: A stability theorem for the obstacle problem. Adv. Math.16, 34–47 (1975)

    Google Scholar 

  17. Schaeffer, D.: Some examples of singularities in a free boundary. Ann. Scuola Norm. Sup. Pisa4, 133–144 (1977)

    Google Scholar 

  18. Schwartz, J.: Nonlinear functional analysis. Courant Institute Lecture Notes, 1965

  19. Stein, E., Weiss, G.: Fourier analysis on euclidean spaces. Princeton, Princeton University Press 1971

    Google Scholar 

  20. 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. Mathematics Department, Princeton University, 08544, Princeton, NJ, USA

    Eric Bedford (Sloan Fellow)

Authors
  1. Eric Bedford
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bedford, E. Stability of envelopes of holomorphy and the degenerate Monge-Ampère equation. Math. Ann. 259, 1–28 (1982). https://doi.org/10.1007/BF01456826

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01456826

Search

Navigation