Sur les remplissages holomorphes équivariants

Kloeckner, Benoît

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).

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

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