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ArticleOriginal scientific text

Title

Weak solutions of equations of complex Monge-Ampère type

Authors 1

Affiliations

  1. Technical University of Łódź, Branch in Bielsko-Biała, Willowa 2, 43-300 Bielsko-Biała, Poland

Abstract

We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.

Keywords

ENG
plurisubharmonic function, complex Monge-Ampère operator

Bibliography

  1. [A1] T. Aubin, Equations du type Monge-Ampère sur les variétés kählériennes compactes, C. R. Acad. Sci. Paris 283 (1976), 119-121.
  2. [A2] T. Aubin, Equations du type Monge-Ampère sur les variétés kählériennes compactes, Bull. Sci. Math. 102 (1978), 63-95.
  3. [A3] T. Aubin, Nonlinear Analysis on Manifolds. Monge-Ampère Equations, Grundlehren Math. Wiss. 244, Springer, 1982.
  4. [BT1] E. Bedford and B. A. Taylor, The Dirichlet problem for the complex Monge-Ampère operator, Invent. Math. 37 (1976), 1-44.
  5. [BT2] E. Bedford and B. A. Taylor, The Dirichlet problem for an equation of complex Monge-Ampère type, in: Partial Differential Equations and Geometry, C. Byrnes (ed.), Dekker, 1979, 39-50.
  6. [BT3] E. Bedford and B. A. Taylor, A new capacity for plurisubharmonic functions, Acta Math. 149 (1982), 1-40.
  7. [BT4] E. Bedford and B. A. Taylor, Uniqueness for the complex Monge-Ampère equation for functions of logarithmic growth, Indiana Univ. Math. J. 38 (1989), 455-469.
  8. L. Caffarelli, J. J. Kohn, L. Nirenberg and J. Spruck, The Dirichlet problem for nonlinear second-order elliptic equations. II. Complex Monge-Ampère, and uniformly elliptic, equations, Comm. Pure Appl. Math. 38 (1985), 209-252.
  9. [Ce] U. Cegrell, On the Dirichlet problem for the complex Monge-Ampère operator, Math. Z. 185 (1984), 247-251.
  10. [K1] S. Kołodziej, The range of the complex Monge-Ampère operator II, Indiana Univ. Math. J. 44 (1995), 765-782.
  11. [K2] S. Kołodziej, Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator, Ann. Polon. Math. 65 (1996), 11-21.
  12. [K3] S. Kołodziej, The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117.
  13. [S] Y.-T. Siu, Lectures on Hermitian-Einstein Metrics for Stable Bundles and Kähler-Einstein Metrics, Birkhäuser, 1987.
  14. [Y] S.-T. Yau, On the Ricci curvature of a compact Kähler manifold and the complex Monge-Ampère equation, Comm. Pure Appl. Math. 31 (1978), 339-411.
Annales Polonici Mathematici
2000/73/1
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Pages:
59-67
Main language of publication
English
Received
1999-01-19
Accepted
1999-11-29
Published
2000
Exact and natural sciences