no. 17-18
Complex Analysis
Special polyhedra for Reinhardt domains
[Polyèdres spéciaux pour des domaines de Reinhardt]

Présenté par : Jean-Pierre Demailly

Rashkovskii, Alexander1 ; Zakharyuta, Vyacheslav2
1 Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway
2 Sabanci University, 34956 Tuzla, Istanbul, Turkey
Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 965-968.

Nous montrons que tout domaine de Reinhardt borné et hyperconvexe est approché extérieurement par des polyèdres polynomiaux spéciaux définis par des applications polynomiales homogènes. Ceci se fait à lʼaide dʼune certaine approximation de la fonction de Green pluricomplexe du domaine avec pôle à lʼorigine.

We show that every bounded hyperconvex Reinhardt domain can be approximated by special polynomial polyhedra defined by homogeneous polynomial mappings. This is achieved by means of approximation of the pluricomplex Green function of the domain with pole at the origin.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.08.009
Rashkovskii, Alexander 1 ; Zakharyuta, Vyacheslav 2

1 Faculty of Science and Technology, University of Stavanger, N-4036 Stavanger, Norway
2 Sabanci University, 34956 Tuzla, Istanbul, Turkey 
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Rashkovskii, Alexander; Zakharyuta, Vyacheslav. Special polyhedra for Reinhardt domains. Comptes Rendus. Mathématique, Tome 349 (2011) no. 17-18, pp. 965-968. doi : 10.1016/j.crma.2011.08.009. http://www.numdam.org/articles/10.1016/j.crma.2011.08.009/

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