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Proceedings of the American Mathematical Society

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Prolongement de courants positifs
a travers de petits obstacles


Authors: Jean-Baptiste Poly and Gilles Raby
Journal: Proc. Amer. Math. Soc. 127 (1999), 2091-2098
MSC (1991): Primary 32C30, 32D15, 53C65, 32C25
DOI: https://doi.org/10.1090/S0002-9939-99-04890-X
Published electronically: March 16, 1999
MathSciNet review: 1605933
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Abstract: In this paper, we prove an extension theorem through closed subsets having small Haussdorff dimension, for positive currents whose boundary satisfies some growth condition. As a corollary, we get the classical Harvey's extension theorem for closed positive currents. Furthermore, we apply our result to study the boundary of holomorphic chains.


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Jean-Baptiste Poly
Affiliation: ESA CNRS 6086 Groupes de Lie et Géométrie, Laboratoire de Mathematiques, Universite de Poitiers, 40 Avenue du Recteur Pineau, 86022 Poitiers, France
Email: poly@wallis.univ-poitiers.fr

Gilles Raby
Affiliation: ESA CNRS 6086 Groupes de Lie et Géométrie, Laboratoire de Mathematiques, Universite de Poitiers, 40 Avenue du Recteur Pineau, 86022 Poitiers, France
Email: raby@mathrs.univ-poitiers.fr

DOI: https://doi.org/10.1090/S0002-9939-99-04890-X
Keywords: Courants positifs, prolongement, mesure de Haussdorff, cha{\^\i}nes holomorphes
Received by editor(s): October 14, 1997
Published electronically: March 16, 1999
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society