Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive

Deroin, Bertrand

Deroin, Bertrand

Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005), p. 57-75 / Harvested from Numdam

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Publié le : 2005-01-01

MR 2136481 | Zbl 1070.37031 | 1 citation dans Numdam

DOI : https://doi.org/10.1016/j.ansens.2004.10.004

@article{ASENS_2005_4_38_1_57_0,
     author = {Deroin, Bertrand},
     title = {Hypersurfaces Levi-plates immerg\'ees dans les surfaces complexes de courbure positive},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {38},
     year = {2005},
     pages = {57-75},
     doi = {10.1016/j.ansens.2004.10.004},
     mrnumber = {2136481},
     zbl = {1070.37031},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/ASENS_2005_4_38_1_57_0}
}

Deroin, Bertrand. Hypersurfaces Levi-plates immergées dans les surfaces complexes de courbure positive. Annales scientifiques de l'École Normale Supérieure, Tome 38 (2005) pp. 57-75. doi : 10.1016/j.ansens.2004.10.004. http://gdmltest.u-ga.fr/item/ASENS_2005_4_38_1_57_0/

Bibliographie

[1] Ahlfors L., Zur Theorie der Überlagerungflächen, Acta Math. 65, 157-194. | JFM 61.0365.03 | MR 1555403 | Zbl 0012.17204

[2] Arnold V., Équations différentielles ordinaires, vol. 2, Mir, Moscow. | MR 361232 | Zbl 0296.34002

[3] Berndtsson B., Sibony N., The $\bar{\partial}$ -equation on a positive current, Invent. Math. 147 (2) (2002) 371-428. | MR 1881924 | Zbl 1031.32005

[4] Camacho C., Lins Neto A., Sad P., Minimal sets of foliations on complex projective spaces, Inst. Hautes Études Sci. Publ. Math. 68 (1988) 187-203. | Numdam | MR 1001454 | Zbl 0682.57012

[5] Bonatti C., Langevin R., Moussu R., Feuilletages de $C P (n)$ : de l’holonomie hyperbolique pour les minimaux exceptionnels, Inst. Hautes Études Sci. Publ. Math. 75 (1992) 123-134. | Numdam | Zbl 0782.32023

[6] Candel A., Uniformization of surface laminations, Ann. Sci. École Norm. Sup. (4) 26 (4) (1993) 489-516. | Numdam | MR 1235439 | Zbl 0785.57009

[7] Candel A., The harmonic measures of Lucy Garnett, Adv. Math. 176 (2) (2003) 187-247. | MR 1982882 | Zbl 1031.58003

[8] Cao J., Shaw M.C., Wang L., Estimates for the $\bar{\partial}$ -Neumann problem and nonexistence of $C^{2}$ Levi-flat hypersurfaces in $C P^{n}$ , Math. Z. (2004). | Zbl 1057.32012

[9] Cerveau D., Minimaux des feuilletages algébriques de $C P (n)$ , Ann. Inst. Fourier 43 (5) (1993) 1535-1543. | Numdam | MR 1275208 | Zbl 0803.32018

[10] Connes A., A survey of foliations and operator algebras, in: Proc. of Symp. Pure Math., vol. 38, Amer. Math. Soc., Providence, RI, 1982, pp. 521-628. | MR 679730 | Zbl 0531.57023

[11] Deroin B., Laminations par variétés complexes, Thèse ENS Lyon, 2003.

[12] Deroin B., Laminations dans les espaces projectifs complexes, math.CV/0410376.

[13] Frankel S., Harmonic analysis of surface group representations to $Diff (S^{1})$ and Milnor type inequalities, Prépublication de l'École Polytechnique 1125, 1996.

[14] Garnett L., Foliations, the ergodic theorem and Brownian motion, J. Funct. Anal. 51 (3) (1983) 285-311. | MR 703080 | Zbl 0524.58026

[15] Ghys É., Gauss-Bonnet theorem for 2-dimensional foliations, J. Funct. Anal. 77 (1) (1988) 51-59. | MR 930390 | Zbl 0656.57017

[16] Hurder S., Mitsumatsu Y., The intersection product of transverse invariant measures, Indiana Univ. Math. J. 40 (4) (1991) 1169-1183. | MR 1142709 | Zbl 0769.57018

[17] Iordan A., On the non-existence of smooth Levi-flat hypersurfaces in $C P^{n}$ , in: Proceedings of the Memorial Conference of K. Oka's centennial birthday on Complex Analysis in Several Variables, Kyoto, Nara, 2001. | Zbl 1073.32019

[18] Malliavin P., Diffusions et géométrie différentielle globale, Centro Internationale Matematico Estivo, Varenne, France, août 1975. | MR 651927

[19] Mañé R., Sad P., Sullivan D., On the dynamics of rational maps, Ann. Sci. École Norm. Sup. (4) 16 (2) (1983) 193-217. | Numdam | MR 732343 | Zbl 0524.58025

[20] Ohsawa T., Sibony N., Kähler identity on Levi-flat manifolds and application to the embedding, Nagoya Math. J. 158 (2000) 87-93. | MR 1766573 | Zbl 0976.32021

[21] Rudin W., Analyse réelle et complexe, Masson, Paris. | MR 662565 | Zbl 00865232

[22] Siu Y.-T., $\bar{\partial}$ -Regularity for weakly pseudoconvex domains in compact hermitian symmetric spaces with respect to invariant metrics, Ann. of Math. 156 (2) (2002) 595-621. | MR 1933078 | Zbl 1030.53071

[23] Sullivan D., Cycles for the dynamical study of foliated manifolds and complex manifolds, Invent. Math. 36 (1976) 225-255. | MR 433464 | Zbl 0335.57015

[24] Sullivan D., Thurston W., Extending holomorphic motions, Acta Math. 157 (3-4) (1986) 243-257. | MR 857674 | Zbl 0619.30026