Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-24T08:03:26.240Z Has data issue: false hasContentIssue false
  • English
  • Français

Complex Monge-Ampère Measures of Plurisubharmonic Functions with Bounded Values Near the Boundary

Published online by Cambridge University Press:  20 November 2018

Yang Xing
Yang Xing*
Affiliation:
Department of Mathematics, University of Umeå, S-901 87 Umeå, Sweden email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We give a characterization of bounded plurisubharmonic functions by using their complex Monge-Ampère measures. This implies a both necessary and sufficient condition for a positive measure to be complex Monge-Ampère measure of some bounded plurisubharmonic function.

Keywords

32F0732F05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 52 , Issue 5 , 01 October 2000 , pp. 1085 - 1100
Copyright
Copyright © Canadian Mathematical Society 2000

References

[B] Bedford, E., Survey of pluri-potential theory. Several Complex Variables: Proceedings of theMittag-Leffler Inst. 1987–1988, (ed. John Erik Fornaess), Math. Notes 38, Princeton Univ. Press, 1993.Google Scholar
[B-T1] Bedford, E. and Taylor, B. A., The Dirichlet problem for the complexMonge-Ampère operator. Invent.Math. 37(1976), 1–44.Google Scholar
[B-T2] Bedford, E. and Taylor, B. A., A new capacity for plurisubharmonic functions. Acta Math. 149(1982), 1–40.Google Scholar
[B-T3] Bedford, E. and Taylor, B. A., Fine topology, Šilov boundary and (ddc)n. J. Funct. Anal. 72(1987), 225–251.Google Scholar
[B-T4] Bedford, E. and Taylor, B. A., Plurisubharmonic functions with logarithmic singularities. Ann. Inst. Fourier (Grenoble) (4) 38(1988), 133–171.Google Scholar
[C1] Cegrell, U., Sums of continuous plurisubharmonic functions and the complex Monge–Ampère operator. Math. Z. 193(1986), 373–380.Google Scholar
[C2] Cegrell, U., Pluricomplex energy. ActaMath. 180(1998), 187–217.Google Scholar
[C-P] Cegrell, U. and Persson, L., The Dirichlet problem for the complex Monge-Ampère operator: stability in L2. Michigan Math. J. 39(1992), 145–151.Google Scholar
[D] Demailly, J.-P., Monge-Ampère operators, Lelong numbers and intersection theory. In: Complex Analysis and Geometry, Univ. Ser. Math., Plenum, New York, 1993, 115–193.Google Scholar
[K] Kiselman, C. O., Sur la definition de l’opérateur deMonge-Ampère complexe. Analyse Complexe: Proceedings, Toulouse (1983), 139–150, Lecture Notes in Math. 1094, Springer-Verleg.Google Scholar
[KO1] Kolodziej, S., The range of the complex Monge-Ampère operator, II. Indiana Univ.Math. J. 44(1995), 765–782.Google Scholar
[KO2] Kolodziej, S., The range of the complex Monge-Ampère operator. Indiana Univ.Math. J. 43(1994), 1321–1338.Google Scholar
[KO3] Kolodziej, S., Some sufficient conditions for solvability of the Dirichlet problem for the complex Monge-Ampère operator. Ann. Polon. Math. 65(1996), 11–21.Google Scholar
[KO4] Kolodziej, S., The complex Monge-Ampère equation. ActaMath. 180(1998), 69–117.Google Scholar
[P] Persson, L., On the Dirichlet problem for the complex Monge-Ampère operator. Thesis, Ume°a, 1992.Google Scholar
[S] Sibony, N., Quelques problémes de prolongement de courants en analyse complexe. DukeMath. J. 52(1985), 157–197.Google Scholar
[X] Xing, Y., Continuity of the complex Monge-Ampère operator. Proc. Amer.Math. Soc. 124(1996), 457–467.Google Scholar