Sur les rétractes holomorphes de dimension 1
Vigué, Jean-Pierre
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998), p. 31-41 / Harvested from Biblioteca Digitale Italiana di Matematica
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In this Note, I study existence and unicity of holomorphic retractions on complex submanifolds of dimension 1.

In questa Nota, vengono studiate l’esistenza e l’unicità di retratti olomorfi su sottovarietà complesse di dimensione 1.

Publié le : 1998-03-01
@article{RLIN_1998_9_9_1_31_0,
     author = {Jean-Pierre Vigu\'e},
     title = {Sur les r\'etractes holomorphes de dimension 1},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {9},
     year = {1998},
     pages = {31-41},
     zbl = {0932.32025},
     mrnumber = {1669248},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/RLIN_1998_9_9_1_31_0}
}

Vigué, Jean-Pierre. Sur les rétractes holomorphes de dimension 1. Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 9 (1998) pp. 31-41. http://gdmltest.u-ga.fr/item/RLIN_1998_9_9_1_31_0/

[1] Belkhchicha, L., Caractérisation des isomorphismes analytiques de certains domaines bornés. C. R. Acad. Sc. Paris, s. I, Math., 313, 1991, 281-284. | MR 1126396 | Zbl 0739.32026

[2] Belkhchicha, L., Caractérisation des isomorphismes analytiques sur la boule-unité de Cn pour une norme. Math. Z., 215, 1994, 129-141. | MR 1254816 | Zbl 0801.32009

[3] Cartan, H., Sur les fonctions de plusieurs variables complexes: l’itérations des transformations intérieures d’un domaine borné. Math. Z., 35, 1932, 760-773. | MR 1545327 | Zbl 0004.40602

[4] Cartan, H., Sur les rétractions d’une variété. C.R. Acad. Sc. Paris, s. I, Math., 303, 1986, 715-716. | MR 870703 | Zbl 0609.32021

[5] Dineen, S., The Schwarz Lemma. Oxford Math. Monographs, Clarendon Press, Oxford1989. | MR 1033739 | Zbl 0708.46046

[6] Dineen, S., Convexity in complex analysis. In: P. Jakobczak - W. Pleasniak (eds.), Topics in complex analysis. Banach Center Publications, 31, Warszawa 1995, 151-162. | MR 1341385 | Zbl 0842.32019

[7] Eisenman, D., Intrinsic measures on complex manifolds. MemoirsAmer. Math. Soc., 96, 1970. | Zbl 0197.05901

[8] Franzoni, T. - Vesentini, E., Holomorphic maps and invariant distances. Math. Studies, 40, North-Holland, Amsterdam-New York 1980. | MR 563329 | Zbl 0447.46040

[9] Gentili, G., On non-uniqueness of complex geodesics in convex bounded domains. Atti Acc. Lincei Rend. fis., s. 8, v. 79, 1985, 90-97. | MR 944377 | Zbl 0637.46018

[10] Gentili, G., On complex geodesics of balanced convex domains. Ann. Mat. Pura et Appl., 144, 1986, 113-130. | MR 870872 | Zbl 0619.32015

[11] Harris, L., Schwarz-Pick systems of pseudometrics for domains in normed linear spaces. In: J. A. Barroso (ed.), Advances in Holomorphy. Proceedings of the Seminario de Holomorfia (Rio de Janeiro, 26-28 September 1977). Math. Studies, 34, North-Holland, Amsterdam-New York 1979, 345-406. | MR 520667 | Zbl 0409.46053

[12] Heath, L. - Suffridge, T., Holomorphic retracts in complex n-space. Illinois J. Math., 25, 1981, 125-135. | MR 602903 | Zbl 0463.32008

[13] Jarnicki, M. - Pflug, P., Invariant distances and metrics in complex analysis. De Gruyter Expositions in Mathematics, 9, Walter de Gruyter, Berlin-New York 1993. | MR 1242120 | Zbl 0789.32001

[14] Kiernan, P., On the relations between taut, tight and hyperbolic manifolds. Bull. Amer. Math. Soc., 76, 1970, 49-51. | MR 252678 | Zbl 0192.44103

[15] Kobayashi, S., Intrinsic distances, measures and geometric function theory. Bull. Amer. Math. Soc., 82, 1976, 357-416. | MR 414940 | Zbl 0346.32031

[16] Lempert, L., La métrique de Kobayashi et la représentation des domaines sur la boule. Bull. Soc. Math. Fr., 109, 1981, 427-474. | MR 660145 | Zbl 0492.32025

[17] Lempert, L., Holomorphic retracts and intrinsic metrics in convex domains. Anal. Math., 8, 1982, 257-261. | MR 690838 | Zbl 0509.32015

[18] Royden, H. - Wong, P., Carathéodory and Kobayashi metrics on convex domains. Preprint 1983.

[19] Thorp, E. - Whitley, R., The strong maximum modulus theorem for analytic functions into a Banach space. Proc. Amer. Math. Soc., 18, 1967, 640-646. | MR 214794 | Zbl 0185.20102

[20] Vesentini, E., Complex geodesics. Compositio Math., 44, 1981, 375-394. | MR 662466 | Zbl 0488.30015

[21] Vesentini, E., Complex geodesics and holomorphic mappings. Symposia Math., 26, 1982, 211-230. | MR 663034 | Zbl 0506.32008

[22] Vesentini, E., Invariant distances and invariant differential metrics in locally convex spaces. In: W. Zelazko (ed.), Spectral Theory. Banach Center Publications, 8, Warszawa 1982, 493-512. | MR 738313 | Zbl 0505.32020

[23] Vigué, J.-P., Sur les points fixes d’applications holomorphes. C. R. Acad. Sc. Paris, I, Math., 303, 1986, 927-930. | MR 873396 | Zbl 0607.32016

[24] Wu, H., Normal families of holomorphic mappings. Acta Math., 119, 1967, 194-233. | MR 224869 | Zbl 0158.33301