no. 6
Sur les remplissages holomorphes équivariants
[On equivariant holomorphic fillings]
Kloeckner, Benoît1
1 ENS de Lyon UMPA 46, allée d’Italie 69364 Lyon Cedex 07 (France)
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) 
@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},
     mrnumber = {2377896},
     zbl = {1132.32014},
     language = {fr},
     url = {https://aif.centre-mersenne.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  - https://aif.centre-mersenne.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 https://aif.centre-mersenne.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. https://aif.centre-mersenne.org/articles/10.5802/aif.2323/

[1] Barth, Wolf P.; Hulek, Klaus; Peters, Chris A. M.; Van de Ven, Antonius Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], 4, Springer-Verlag, Berlin, 2004 | MR | Zbl

[2] D’Angelo, John P. Several complex variables and the geometry of real hypersurfaces, Studies in Advanced Mathematics, CRC Press, Boca Raton, FL, 1993 | Zbl

[3] Eliashberg, Yakov Filling by holomorphic discs and its applications, Geometry of low-dimensional manifolds, 2 (Durham, 1989) (London Math. Soc. Lecture Note Ser.), Volume 151, Cambridge Univ. Press, Cambridge, 1990, pp. 45-67 | MR | Zbl

[4] Giraud, Georges Sur certaines fonctions automorphes de deux variables, Ann. Sci. École Norm. Sup. (3), Volume 38 (1921), pp. 43-164 | Numdam | MR

[5] Goldman, William M. Complex hyperbolic geometry, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1999 (, Oxford Science Publications) | MR | Zbl

[6] Griffiths, Phillip; Harris, Joseph Principles of algebraic geometry, Wiley Classics Library, John Wiley & Sons Inc., New York, 1994 (Reprint of the 1978 original) | MR | Zbl

[7] Khenkin, G. M. Several complex variables. III, Encyclopaedia of Mathematical Sciences, 9, Springer-Verlag, Berlin, 1989 Geometric function theory, A translation of Sovremennye problemy matematiki. Fundamentalnye napravleniya, Tom 9, Akad. Nauk SSSR, Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1986 [ MR0860607 (87m :32011)], Translation by J. Peetre, Translation edited by G. M. Khenkin | MR | Zbl

[8] Kulkarni, Ravi S. Conjugacy classes in M(n), Conformal geometry (Bonn, 1985/1986) (Aspects Math., E12), Vieweg, Braunschweig, 1988, pp. 41-64 | MR | Zbl

[9] McMullen, Curtis T. Dynamics on K3 surfaces : Salem numbers and Siegel disks, J. Reine Angew. Math., Volume 545 (2002), pp. 201-233 | DOI | MR | Zbl

[10] McMullen, Curtis T. Dynamics on blowups of the projective plane, 2006 (prépublication)

[11] Montgomery, Deane; Zippin, Leo Existence of subgroups isomorphic to the real numbers, Ann. of Math. (2), Volume 53 (1951), pp. 298-326 | DOI | MR | Zbl

[12] Schoen, R. On the conformal and CR automorphism groups, Geom. Funct. Anal., Volume 5 (1995) no. 2, pp. 464-481 | DOI | MR | Zbl

[13] Waterman, P. L. Purely elliptic Möbius groups, Holomorphic functions and moduli, Vol. II (Berkeley, CA, 1986) (Math. Sci. Res. Inst. Publ.), Volume 11, Springer, New York, 1988, pp. 173-178 | MR | Zbl

Cited by Sources: