Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • 1. E.M. Chirka, Complex analytic sets, Kluwer Academic Pub., Dordrecht, 1989. MR 92b:32016
  • 2. H. Federer, Geometric measure theory, Springer-Verlag, New-York, 1969. MR 41:1976
  • 3. R. Harvey, Removable singularities for positive currents, Amer. J. Math. 96 (1974), 67-78. MR 50:13602
  • 4. R. Harvey, Holomorphic chains and their boundaries, Proc. Symp. Pure Math. 30 Part 1 (1977), 309-382. MR 56:5929
  • 5. R. Harvey and B. Lawson, On boundaries of complex analytic varieties , Ann. of Math. 102 (1975), 233-290. MR 54:13130
  • 6. R. Harvey and B. Lawson, On boundaries of complex analytic varieties , Ann. of Math. 106 (1977), 213-238. MR 58:17186
  • 7. J. King, The currents defined by analytic varieties, Acta Math. 127 (1971), 185-220. MR 52:14359
  • 8. P. Lelong, Intégration sur un ensemble analytique complexe, Bull. Soc. Math. France 85 (1957), 239-262. MR 20:2465
  • 9. V. Maz'ja, Sobolev spaces, Springer-Verlag, Berlin, 1985. MR 87g:46056
  • 10. B. Shiffman, On the removal of singularities of analytic sets, Michigan Math. J. 15 (1968), 111-120. MR 37:464

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 32C30, 32D15, 53C65, 32C25

Retrieve articles in all journals with MSC (1991): 32C30, 32D15, 53C65, 32C25


Additional Information

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

American Mathematical Society