Skip to main content
SpringerLink
Log in

Pluripotential theory for convex bodies in RN

  • Published:
Mathematische Zeitschrift 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. Bagby, T., Levenberg, N.:Bernstein theorems for harmonic functions. Methods of Approx. Theory in Complex Analysis and Mathematical Physics, Lecture Notes in Math. (Springer-Verlag), 1550, 7–18 (1993)

    Google Scholar 

  2. Baran, M.: Siciak’s extremal function of convex sets in Cn. Annales Polonici Math. 48, 275–280 (1988)

    MATH  Google Scholar 

  3. Baran, M.: Plurisubharmonic extremal functions and complex foliations for the complement of convex sets in Rn. Michigan Math. J. 39, 395–404 (1992)

    Article  MATH  Google Scholar 

  4. Bedford, E., Kalka, M.: Foliations and complex Monge-Ampère equations, Comm. Pure Appl. Math. 30(5), 543–571 (1977)

    MATH  Google Scholar 

  5. Bloom, T., Levenberg, N., Ma’u, S.: Robin functions and extremal functions. Annales Polonici Math. 80, 55–84 (2003)

    MATH  Google Scholar 

  6. Borell, S.: Pluricomplex Green functions and invariant pseudodistances in convex domains. Mid Sweden University Masters Thesis

  7. Bos, L., Calvi, J.-P., Levenberg, N.: On the Siciak extremal function for real compact convex sets in RN. Arkiv for Mat. 39(2), 245–262 (2001)

    MATH  Google Scholar 

  8. Klimek, M.: Pluripotential Theory. Oxford University Press, Oxford, 1991

  9. Klimek, M.: Metrics associated with extremal plurisubharmonic functions. Proc. Amer. Math. Soc. 123, 2763–2770 (1995)

    MATH  Google Scholar 

  10. Lempert, L.: La métrique de Kobayashi et la représentation des domaines sur la boule. Bull. Soc. Math. France 109(4), 427–474 (1981)

    MATH  Google Scholar 

  11. Lempert, L.: Symmetries and other transformations of the complex Monge-Ampre equation. Duke Math. J. 52(4), 869–885 (1985)

    MATH  Google Scholar 

  12. Lempert, L.: Intrinsic distances and holomorphic retracts. Complex analysis and applications ‘81 (Varna, 1981), 1984, pp. 341–364

  13. Lundin, M.: The extremal plurisubharmonic function for the complement of convex, symmetric subsets of Rn. Michigan Math. J. 32, 197–201 (1985)

    Article  MATH  Google Scholar 

  14. Lundin, M.: Thesis (unpublished)

  15. Ma’u, S.: Plurisubharmonic functions of logarithmic growth. PhD thesis, University of Auckland, 2003

  16. Ma’u, S.: Plurisubharmonic functions characterized by one-variable extremal functions. Preprint

  17. Momm, S.: An extremal plurisubharmonic function associated to a convex pluricomplex Green function with pole at infinity. J. Reine Angew. Math. 471, 139–163 (1996)

    MATH  Google Scholar 

  18. Nguyen Thanh Van Djebbar, B.: Propriétés asymptotiques d’une suite orthonormale de polynômes harmoniques. Bull. Sc. Math. 113, 239–251 (1989)

    Google Scholar 

  19. Ransford, T.: Potential Theory in the Complex Plane. Cambridge Univ. Press, Cambridge, 1995

  20. Siciak, J.: Extremal plurisubharmonic functions in CN. Annales Polonici Math. 39, 175–211 (1981)

    MATH  Google Scholar 

  21. Walsh, J.L.: Maximal convergence of sequences of harmonic polynomials. Ann. Math. 38, 321–354 (1936)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, Michigan, 48109-1109, USA

    D. Burns

  2. Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, New Zealand

    N. Levenberg & S. Ma’u

  3. Department of Mathematics, Indiana University, Bloomington, Indiana, 47405, USA

    N. Levenberg

Authors
  1. D. Burns
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. Levenberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Ma’u
    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

Burns, D., Levenberg, N. & Ma’u, S. Pluripotential theory for convex bodies in RN. Math. Z. 250, 91–111 (2005). https://doi.org/10.1007/s00209-004-0743-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-004-0743-z

Keywords

Search

Navigation