Weak solutions of equations of complex Monge-Ampère type

Sławomir Kołodziej

Annales Polonici Mathematici (2000)

  • Volume: 73, Issue: 1, page 59-67
  • ISSN: 0066-2216

Abstract

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

How to cite

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Kołodziej, Sławomir. "Weak solutions of equations of complex Monge-Ampère type." Annales Polonici Mathematici 73.1 (2000): 59-67. <http://eudml.org/doc/262805>.

@article{Kołodziej2000,
abstract = {We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.},
author = {Kołodziej, Sławomir},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic function; complex Monge-Ampère operator; plurisubharmonic functions},
language = {eng},
number = {1},
pages = {59-67},
title = {Weak solutions of equations of complex Monge-Ampère type},
url = {http://eudml.org/doc/262805},
volume = {73},
year = {2000},
}

TY - JOUR
AU - Kołodziej, Sławomir
TI - Weak solutions of equations of complex Monge-Ampère type
JO - Annales Polonici Mathematici
PY - 2000
VL - 73
IS - 1
SP - 59
EP - 67
AB - We prove some existence results for equations of complex Monge-Ampère type in strictly pseudoconvex domains and on Kähler manifolds.
LA - eng
KW - plurisubharmonic function; complex Monge-Ampère operator; plurisubharmonic functions
UR - http://eudml.org/doc/262805
ER -

References

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  2. [A2] T. Aubin, Equations du type Monge-Ampère sur les variétés kählériennes compactes, Bull. Sci. Math. 102 (1978), 63-95. Zbl0374.53022
  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. Zbl0315.31007
  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. Zbl0547.32012
  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. Zbl0677.32002
  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. Zbl0598.35048
  9. [Ce] U. Cegrell, On the Dirichlet problem for the complex Monge-Ampère operator, Math. Z. 185 (1984), 247-251. Zbl0539.35001
  10. [K1] S. Kołodziej, The range of the complex Monge-Ampère operator II, Indiana Univ. Math. J. 44 (1995), 765-782. Zbl0849.31009
  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. Zbl0878.32014
  12. [K3] S. Kołodziej, The complex Monge-Ampère equation, Acta Math. 180 (1998), 69-117. Zbl0913.35043
  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. Zbl0369.53059

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