Sur les remplissages holomorphes équivariants
[On equivariant holomorphic fillings]
Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 2041-2061.

We study the fillings of a three-dimensional CR manifold by a complex surface, under an equivariance hypothesis. Namely, we assume that many automorphisms of the CR manifold admit a biholomorphic extension to the whole filling. When the CR manifold is strictly pseudoconvex, we prove a uniqueness result (up to a blow-up).

On étudie les remplissages d’une variété CR de dimension trois par une surface complexe, sous une hypothèse d’équivariance : on suppose que beaucoup d’automorphismes CR du bord se prolongent en des biholomorphismes de tout le remplissage. On démontre dans le cas strictement pseudoconvexe un résultat d’unicité (à éclatement près).

DOI: 10.5802/aif.2323
Classification: 32V30
Mot clés : remplissages, variétés CR stictement pseudoconvexes, surfaces complexes, action de groupe non compact
Keywords: fillings, strictly pseudoconvex CR manifold, complex surfaces, non-compact group action
Kloeckner, Benoît 1

1 ENS de Lyon UMPA 46, allée d’Italie 69364 Lyon Cedex 07 (France)
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Kloeckner, Benoît. Sur les remplissages holomorphes équivariants. Annales de l'Institut Fourier, Volume 57 (2007) no. 6, pp. 2041-2061. doi : 10.5802/aif.2323. https://aif.centre-mersenne.org/articles/10.5802/aif.2323/

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