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).
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
@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{\textquoteright}institut Fourier}, volume = {57}, number = {6}, year = {2007}, doi = {10.5802/aif.2323}, zbl = {1132.32014}, mrnumber = {2377896}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2323/} }
TY - JOUR AU - Kloeckner, Benoît TI - Sur les remplissages holomorphes équivariants JO - Annales de l'Institut Fourier PY - 2007 SP - 2041 EP - 2061 VL - 57 IS - 6 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2323/ DO - 10.5802/aif.2323 LA - fr ID - AIF_2007__57_6_2041_0 ER -
%0 Journal Article %A Kloeckner, Benoît %T Sur les remplissages holomorphes équivariants %J Annales de l'Institut Fourier %D 2007 %P 2041-2061 %V 57 %N 6 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2323/ %R 10.5802/aif.2323 %G fr %F AIF_2007__57_6_2041_0
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. http://archive.numdam.org/articles/10.5802/aif.2323/
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