Attenuating the singularities of plurisubharmonic functions
Christer O. Kiselman
Annales Polonici Mathematici, Tome 60 (1994), p. 173-197 / Harvested from The Polish Digital Mathematics Library
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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.

Resumo (Malfortigi la malregulejojn la plursubharmonaj funkcioj). Ni studas la malregulejojn de la plursubharmonaj funkcioj per metodoj de la konveksa analitiko. Teoremoj pri analitikeco de rafinita nombro de Lelong estas pruvitaj.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:262449 
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     year = {1994},
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Christer O. Kiselman. Attenuating the singularities of plurisubharmonic functions. Annales Polonici Mathematici, Tome 60 (1994) pp. 173-197. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv60z2p173bwm/

[000] L. Abrahamsson [1988], Microlocal Lelong numbers of plurisubharmonic functions, J. Reine Angew. Math. 388, 116-128. | Zbl 0641.31005

[001] J.-P. Demailly [1987], Nombres de Lelong généralisés, théorèmes d'intégralité et d'analyticité, Acta Math. 159, 153-169. | Zbl 0629.32011

[002] L. Hörmander [1990], Complex Analysis in Several Variables, North-Holland. | Zbl 0685.32001

[003] C. O. Kiselman [1978], The partial Legendre transformation for plurisubharmonic functions, Invent. Math. 49, 137-148. | Zbl 0378.32010

[004] C. O. Kiselman [1979], Densité des fonctions plurisousharmoniques, Bull. Soc. Math. France 107, 295-304. | Zbl 0416.32007

[005] 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.

[006] 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.

[007] P. Lelong [1985], Les objets souples de l'analyse complexe, Exposition. Math. 3, 149-164. | Zbl 0574.32025

[008] Y.-T. Siu [1974], Analyticity of sets associated to Lelong numbers and the extension of closed positive currents, Invent. Math. 27, 53-156. | Zbl 0289.32003

[009] H. Skoda [1972], Sous-ensembles analytiques d’ordre fini ou infini dans ℂn, Bull. Soc. Math. France 100, 353-408. | Zbl 0246.32009

[010] X. Wang [1991], Analyticity theorems for parameter-dependent currents, Math. Scand. 69, 179-198. | Zbl 0770.32008