Some problems on plurisubharmonic singularities

A. Rashkovskii
Tek nat, University of Stavanger, 4036 Stavanger, Norway
We present several related problems on residual Monge-Ampere masses of plurisubharmonic functions.
plurisubharmonic function; Lelong number; Monge-Amp`ere operator
1. P. Ahag, U. Cegrell, Pham Hoang Hiep, Monge-Ampere measures on subvarieties, J. Math. Anal. Appl., 423 (2015), ¹1, 94-105.

2. Z. Blocki, Some applications of the Ohsawa-Takegoshi extension theorem, Expositiones Mathematicae, 27 (2009), 125-135.

3. S. Boucksom, C. Favre, M. Jonsson, Valuations and plurisubharmonic singularities, Publ. Res. Inst. Math. Sci., 44 (2008), ¹2, 449-494.

4. U. Cegrell, The general definition of the complex Monge.Amp`ere operator, Ann. Inst. Fourier (Grenoble), 54 (2004), ¹1, 159-179.

5. J.-P. Demailly, Regularization of closed positive currents and intersection theory, J. Algebraic Geometry, 1 (1992), 361-409.

6. J.P. Demailly, Monge-Amp`ere operators, Lelong numbers and intersection theory, Complex Analysis and Geometry (Univ. Series in Math.), ed. by V. Ancona and A. Silva, Plenum Press, New York 1993, 115.

193. Available as Ch. 3 of the Open Content Book: J.P. Demailly, Complex analytic and differential geometry, demailly/manuscripts/agbook.pdf.

7. J.P. Demailly, J. Kollar, Semi-continuity of complex singularity exponents and K”§ahler-Einstein metrics on Fano orbifolds, Ann. Sci. Ecole Norm. Sup., 34 (2001), ¹4, 525-556.

8. J.-P. Demailly, Pham Hoang Hiep, A sharp lower bound for the log canonical threshold, Acta Math., 212 (2014), ¹1, 1-9.

9. S. Dinew, V. Guedj, A. Zeriahi, Open problems in pluripotential theory, Complex Var. Elliptic Equ., (2016); available at

10. C. Favre, V. Guedj, Dynamique des applications rationnelles des espaces multiprojectifs, Indiana Univ. Math. J., 50 (2001), ¹2, 881-934.

11. C.O. Kiselman, Attenuating the singularities of plurisubharmonic functions, Ann. Polon. Math. LX.2 (1994), 173-197.

12. A. Rashkovskii, Plurisubharmonic functions with multicircled singularities, Visnyk Hark. Nats. Univ., 475 (2000), 162-169.

13. A. Rashkovskii, Lelong numbers with respect to regular plurisubharmonic weights, Results Math., 39 (2001), 320-332.

14. A. Rashkovskii, Singularities of plurisubharmonic functions and positive closed currents,

15. A. Rashkovskii, Relative types and extremal problems for plurisubharmonic functions, Int. Math. Res. Not., 2006 (2006), Article ID 76283, 26 p.

16. A. Rashkovskii, Analytic approximations of plurisubharmonic singularities, Math. Z., 275 (2013), Issue 3, 1217-1238.

17. B. Teissier, Sur une in`egalit`e a la Minkowski, Annals Math., 106 (1977), ¹1, 38-44.

18. J. Wiklund, Pluricomplex charge at weak singularities,

19. V.P. Zahariuta, Spaces of analytic functions and Complex Potential Theory, Linear Topological Spaces and Complex Analysis, 1 (1994), 74-146.

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