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Articles

Lelong–Jensen formula, Demailly–Lelong numbers and weighted degree of positive supercurrents

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Pages 1451-1485 | Received 26 Nov 2019, Accepted 24 Apr 2020, Published online: 03 Jun 2020

References

  • Lagerberg A. Super currents and tropical geometry. Math Z. 2012;270:1011–1050. doi: 10.1007/s00209-010-0837-8
  • Berndtsson B. Superforms, supercurrents, minimal manifolds and Riemannian geometry. Arnold Math J. 2019;5:501–532. doi: 10.1007/s40598-019-00130-x
  • Şahin S. M-pluri potential theory on Riemannian spaces and tropical geometry. 2018. Available from: https://arxiv.org/abs/1805.00379.
  • Trudinger NS, Wang X -J. Hessian measures III. J Funct Anal. 2002;193:1–23. doi: 10.1006/jfan.2001.3925
  • Demailly J-P. Complex analytic and differential geometry. 1997. Available from: http://www.fourier.ujf-grenoble.fr/demailly/.
  • Rashkovskii A. Total masses of mixed Monge-Ampère currents. Mich Math J. 2003;51(1):169–185. doi: 10.1307/mmj/1049832899
  • Dabbek K, Elkhadhra F, El Mir H. Extension of plurisubharmonic currents. Math Z. 2003;245:455–481. doi: 10.1007/s00209-003-0538-7
  • Dhouib A, Elkhadhra F. m-potential theory associated to a positive closed current in the class of m-sh functions. Complex Var Elliptic Equ. 2016;61(7):875–901. doi: 10.1080/17476933.2015.1133615
  • Blocki Z. Weak solutions to the complex Hessian equation. Ann Inst Fourier Grenoble. 2018;55(5):1735–1756. doi: 10.5802/aif.2137
  • Wan D, Wang W. Lelong-Jensen type formula, k-Hessian boundary measure and Lelong number for k-convex functions. J Math Pures Appl. 2013;99:635–654. doi: 10.1016/j.matpur.2012.10.002
  • Demailly J-P. Formules de Jensen en plusieurs variables et applications arithmétiques. Bull Soc Math France. 1982;110:75–102. doi: 10.24033/bsmf.1954
  • Skoda H. Prolongement des courants, positifs, fermés de masse finie. Invent Math. 1982;66:361–376. doi: 10.1007/BF01389217
  • Benali A, Ghiloufi N. Lelong numbers of m-subharmonic functions. J Math Anal Appl. 2018;466:1373–1392. doi: 10.1016/j.jmaa.2018.06.055
  • Ghiloufi N. Existence of Lelong numbers of positive plurisuperharmonic currents. Bull Sci Math. 2016;140:64–81. doi: 10.1016/j.bulsci.2014.12.007
  • Elkhadhra F, Mimouni S. A Liouville theorem for plurisubharmonic currents. Ann Facul Sci Toul. 2010;19:651–674. doi: 10.5802/afst.1261
  • Coman D, Nivoche S. Plurisubharmonic functions with singularities and affine invariants for finite sets in Cn. Math Ann. 2002;322:317–332. doi: 10.1007/s002080100272

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