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Potential theory in nevanlinna theory and analytic geometry

  • Robert E. Molzon
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1039)

Keywords

Meromorphic Function Potential Theory Smooth Boundary Equilibrium Measure Extremal Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    H. Alexander: Projective capacity, Conference on Several Complex Variables, Ann. Math. Studies 100, Princeton University Press, Princeton 1981.Google Scholar
  2. [2]
    _____: A note on projective capacity (manuscript).Google Scholar
  3. [3]
    E. Bedford and B.A. Taylor: Potential theoretic properties of plurisubharmonic functions, Acta Math., to appear.Google Scholar
  4. [4]
    J.P. Demailly: Formulas de Jensen en plusieurs variables et applications arithmétiques (manuscript).Google Scholar
  5. [5]
    L. Gruman: Ensembles exceptionnel pour les applications holomorphic dans ℂn, Seminaire Lelong-Skoda 1981, to appear.Google Scholar
  6. [6]
    W. Hayman: Meromorphic Functions, Oxford University Press, Oxford 1968.Google Scholar
  7. [7]
    G.M. Henkin: Solutions with estimates of the H. Lewy and Poincaré-Lelong equations. Construction of functions in the Nevanlinna class with prescribed zeros in strictly pseudoconvex domains, Dokl. Akad. Nauk. SSSR 225, 771–774 (1975).MathSciNetGoogle Scholar
  8. [8]
    J.R. King: The currents defined by analytic varieties, Acta Math. 127, 185–220 (1971).MathSciNetzbMATHCrossRefGoogle Scholar
  9. [9]
    F. Leja: Sur les suites des polynômes bornés presque partout sur la frontiere l'un domaine, Math. Ann. 108, 517–524 (1933).MathSciNetCrossRefGoogle Scholar
  10. [10]
    R. Molzon, B. Shiffman, and N. Sibony: Average growth estimates for hyperplane sections of entire analytic sets, Math. Ann. 257, 43–59 (1981).MathSciNetzbMATHCrossRefGoogle Scholar
  11. [11]
    R. Molzon: Blaschke conditions for holomorphic mappings (manuscript).Google Scholar
  12. [12]
    _____: Potential theory on ℙnℂ: Applications to characterization of pluripolar sets and growth of analytic varieties (manuscript).Google Scholar
  13. [13]
    R. Nevanlinna: Analytic Functions, Springer-Verlag, Berlin, Heidelberg, New York 1970.zbMATHGoogle Scholar
  14. [14]
    W. Rudin: Function Theory in the Unit Ball in ℂn, Springer-Verlag, Berlin, Heidelberg, New York 1980.CrossRefGoogle Scholar
  15. [15]
    H. Skoda: Valeurs au bord pour les solutions de l'operateur d″, et caracterisation des zéros des fonctions de la classe de Nevanlinna, Bull. Soc. Math. France 104, 225–299 (1976).MathSciNetzbMATHGoogle Scholar
  16. [16]
    _____: Solution à croissance du second problème de Cousin dans ℂn, Ann. de L'Institut Fourier 21, 11–23 (1971).MathSciNetzbMATHCrossRefGoogle Scholar
  17. [17]
    J. Siciak: Extremal plurisubharmonic functions in ℂn, Ann. Polonici Math. 39, 175–211 (1981).MathSciNetzbMATHGoogle Scholar
  18. [18]
    _____: Extremal plurisubharmonic functions and capacities in ℂn (manuscript).Google Scholar
  19. [19]
    J. Siciak: On some extremal functions and their applications in the theory of analytic functions of several complex variables, Trans. Amer. Math. Soc. 105, 322–357, (1962).MathSciNetzbMATHCrossRefGoogle Scholar
  20. [20]
    E. Stein: Boundary Behavior of Holomorphic Functions of Several Complex Variables, Princeton University Press, Princeton 1972.zbMATHGoogle Scholar
  21. [21]
    W. Stoll: Value Distribution on Parabolic Spaces, Springer-Verlag, Berlin, Heidelberg, New York 1977.zbMATHGoogle Scholar
  22. [22]
    M. Tsuji: Potential Theory in Modern Function Theory, Maruzen Co., Tokyo 1958.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • Robert E. Molzon
    • 1
  1. 1.Department of MathematicsUniversity of KentuckyLexingtonUSA

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