Attenuating the singularities of plurisubharmonic functions

Christer O. Kiselman

Annales Polonici Mathematici (1994)

  • Volume: 60, Issue: 2, page 173-197
  • ISSN: 0066-2216

Abstract

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We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.

How to cite

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Christer O. Kiselman. "Attenuating the singularities of plurisubharmonic functions." Annales Polonici Mathematici 60.2 (1994): 173-197. <http://eudml.org/doc/262449>.

@article{ChristerO1994,
abstract = {We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.},
author = {Christer O. Kiselman},
journal = {Annales Polonici Mathematici},
keywords = {plurisubharmonic function; analytic variety; convex function; Fenchel transformation; singularities; Lelong number; analyticity theorem},
language = {eng},
number = {2},
pages = {173-197},
title = {Attenuating the singularities of plurisubharmonic functions},
url = {http://eudml.org/doc/262449},
volume = {60},
year = {1994},
}

TY - JOUR
AU - Christer O. Kiselman
TI - Attenuating the singularities of plurisubharmonic functions
JO - Annales Polonici Mathematici
PY - 1994
VL - 60
IS - 2
SP - 173
EP - 197
AB - We study the singularities of plurisubharmonic functions using methods from convexity theory. Analyticity theorems for a refined Lelong number are proved.
LA - eng
KW - plurisubharmonic function; analytic variety; convex function; Fenchel transformation; singularities; Lelong number; analyticity theorem
UR - http://eudml.org/doc/262449
ER -

References

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  1. L. Abrahamsson [1988], Microlocal Lelong numbers of plurisubharmonic functions, J. Reine Angew. Math. 388, 116-128. Zbl0641.31005
  2. J.-P. Demailly [1987], Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité, Acta Math. 159, 153-169. Zbl0629.32011
  3. L. Hörmander [1990], Complex Analysis in Several Variables, North-Holland. Zbl0685.32001
  4. C. O. Kiselman [1978], The partial Legendre transformation for plurisubharmonic functions, Invent. Math. 49, 137-148. Zbl0378.32010
  5. C. O. Kiselman [1979], Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107, 295-304. Zbl0416.32007
  6. C. O. Kiselman [1987], Un nombre de Lelong raffiné, in: Séminaire d'Analyse Complexe et Géométrie 1985-87, Faculté des Sciences de Tunis & Faculté des Sciences et Techniques de Monastir, 61-70. 
  7. C. O. Kiselman [1992], La teoremo de Siu por abstraktaj nombroj de Lelong, in: Aktoj de Internacia Scienca Akademio Comenius, Vol. 1, Beijing, 56-65. 
  8. P. Lelong [1985], Les objets souples de l'analyse complexe, Exposition. Math. 3, 149-164. Zbl0574.32025
  9. Y.-T. Siu [1974], Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27, 53-156. Zbl0289.32003
  10. H. Skoda [1972], Sous-ensembles analytiques d’ordre fini ou infini dans ℂ n , Bull. Soc. Math. France 100, 353-408. Zbl0246.32009
  11. X. Wang [1991], Analyticity theorems for parameter-dependent currents, Math. Scand. 69, 179-198. Zbl0770.32008

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