On the weighted log canonical thresholds of plurisubharmonic functions
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- by Nguyen Xuan Hong PDF
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Abstract:
In this paper, we study the singularities of the plurisubharmonic functions defined on a neighborhood of the origin. We will prove an inequality for the weighted log canonical thresholds of plurisubharmonic functions.References
- Per Åhag, Urban Cegrell, RafałCzyż, and Phạm Hoàng Hiệp, Monge-Ampère measures on pluripolar sets, J. Math. Pures Appl. (9) 92 (2009), no. 6, 613–627 (English, with English and French summaries). MR 2565845, DOI 10.1016/j.matpur.2009.06.001
- P. Åhag, U. Cegrell, S. Kołodziej, H. H. Phạm, and A. Zeriahi, Partial pluricomplex energy and integrability exponents of plurisubharmonic functions, Adv. Math. 222 (2009), no. 6, 2036–2058. MR 2562773, DOI 10.1016/j.aim.2009.07.002
- Urban Cegrell, The general definition of the complex Monge-Ampère operator, Ann. Inst. Fourier (Grenoble) 54 (2004), no. 1, 159–179 (English, with English and French summaries). MR 2069125, DOI 10.5802/aif.2014
- Jean-Pierre Demailly, Estimates on Monge-Ampère operators derived from a local algebra inequality, Complex analysis and digital geometry, Acta Univ. Upsaliensis Skr. Uppsala Univ. C Organ. Hist., vol. 86, Uppsala Universitet, Uppsala, 2009, pp. 131–143 (English, with English and French summaries). MR 2742678
- Jean-Pierre Demailly and Hoàng Hiệp Phạm, A sharp lower bound for the log canonical threshold, Acta Math. 212 (2014), no. 1, 1–9. MR 3179606, DOI 10.1007/s11511-014-0107-4
- Jean-Pierre Demailly and János Kollár, Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds, Ann. Sci. École Norm. Sup. (4) 34 (2001), no. 4, 525–556 (English, with English and French summaries). MR 1852009, DOI 10.1016/S0012-9593(01)01069-2
- Pham Hoang Hiep, The weighted log canonical threshold, C. R. Math. Acad. Sci. Paris 352 (2014), no. 4, 283–288 (English, with English and French summaries). MR 3186914, DOI 10.1016/j.crma.2014.02.010
- Pham Hoang Hiep, Continuity properties of certain weighted log canonical thresholds, C. R. Math. Acad. Sci. Paris 355 (2017), no. 1, 34–39. MR 3590284, DOI 10.1016/j.crma.2016.11.005
- Hoang Hiep Pham, Log canonical thresholds and Monge-Ampère masses, Math. Ann. 370 (2018), no. 1-2, 555–566. MR 3747495, DOI 10.1007/s00208-017-1518-2
- Nguyen Xuan Hong, Semi-continuity properties of weighted log canonical thresholds of toric plurisubharmonic functions, C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 487–492 (English, with English and French summaries). MR 3650372, DOI 10.1016/j.crma.2017.04.014
- Nguyen Xuan Hong, A note on the weighted log canonical thresholds of plurisubharmonic functions, C. R. Math. Acad. Sci. Paris 356 (2018), no. 8, 865–869 (English, with English and French summaries). MR 3851540, DOI 10.1016/j.crma.2018.06.003
- Nguyen Xuan Hong, Tang Van Long and Pham Nguyen Thu Trang, ACC conjecture for weighted log canonical thresholds, to appear in Analysis Mathematica.
- Takeo Ohsawa and Kensh\B{o} Takegoshi, On the extension of $L^2$ holomorphic functions, Math. Z. 195 (1987), no. 2, 197–204. MR 892051, DOI 10.1007/BF01166457
- Alexander Rashkovskii, Extremal cases for the log canonical threshold, C. R. Math. Acad. Sci. Paris 353 (2015), no. 1, 21–24 (English, with English and French summaries). MR 3285141, DOI 10.1016/j.crma.2014.11.002
- Henri Skoda, Sous-ensembles analytiques d’ordre fini ou infini dans $\textbf {C}^{n}$, Bull. Soc. Math. France 100 (1972), 353–408 (French). MR 352517, DOI 10.24033/bsmf.1743
Additional Information
- Nguyen Xuan Hong
- Affiliation: Department of Mathematics, Hanoi National University of Education, 136 Xuan Thuy Street, Cau Giay District, Hanoi, Vietnam
- MR Author ID: 914093
- Email: xuanhongdhsp@yahoo.com
- Received by editor(s): November 16, 2018
- Received by editor(s) in revised form: February 11, 2019, and February 28, 2019
- Published electronically: June 10, 2019
- Additional Notes: This research was funded by the Vietnam Ministry of Education and Training under grant number B2019-SPH-01
- Communicated by: Filippo Bracci
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 147 (2019), 5063-5070
- MSC (2010): Primary 14B05, 32S05, 32U25
- DOI: https://doi.org/10.1090/proc/14624
- MathSciNet review: 4021069