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.
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.
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Published online:
Alexander Rashkovskii 1; Vyacheslav Zakharyuta 2
@article{CRMATH_2011__349_17-18_965_0, author = {Alexander Rashkovskii and Vyacheslav Zakharyuta}, title = {Special polyhedra for {Reinhardt} domains}, journal = {Comptes Rendus. Math\'ematique}, pages = {965--968}, publisher = {Elsevier}, volume = {349}, number = {17-18}, year = {2011}, doi = {10.1016/j.crma.2011.08.009}, language = {en}, }
Alexander Rashkovskii; Vyacheslav Zakharyuta. Special polyhedra for Reinhardt domains. Comptes Rendus. Mathématique, Volume 349 (2011) no. 17-18, pp. 965-968. doi : 10.1016/j.crma.2011.08.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.08.009/
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