Sur les remplissages holomorphes équivariants
Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 2041-2061.

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).

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).

Reçu le : 2006-10-26
Accepté le : 2006-11-30
DOI : https://doi.org/10.5802/aif.2323
Classification : 32V30
Mots clés: remplissages, variétés CR stictement pseudoconvexes, surfaces complexes, action de groupe non compact
@article{AIF_2007__57_6_2041_0,
     author = {Kloeckner, Beno\^\i t},
     title = {Sur les remplissages holomorphes \'equivariants},
     journal = {Annales de l'Institut Fourier},
     pages = {2041--2061},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {6},
     year = {2007},
     doi = {10.5802/aif.2323},
     mrnumber = {2377896},
     zbl = {1132.32014},
     language = {fr},
     url = {aif.centre-mersenne.org/item/AIF_2007__57_6_2041_0/}
}
Kloeckner, Benoît. Sur les remplissages holomorphes équivariants. Annales de l'Institut Fourier, Tome 57 (2007) no. 6, pp. 2041-2061. doi : 10.5802/aif.2323. https://aif.centre-mersenne.org/item/AIF_2007__57_6_2041_0/

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