Geodesic
Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in \( C^{n} \) with real analytic boundary
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 2, pp. 193-196.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

It is shown that given a bounded strictly convex domain \( \Omega \) in \( C^{n} \) with real analitic boundary and a point \( x_{0} \) in \( \Omega \), there exists a larger bounded strictly convex domain \( \Omega ' \) with real analitic boundary, close as wished to \( \Omega \), such that \( \Omega \) is a ball for the Kobayashi distance of \( \Omega ' \) with center \( x_{0} \). The result is applied to prove that if \( \Omega \) is not biholomorphic to the ball then any automorphism of \( \Omega \) extends to an automorphism of \( \Omega ' \).
Si dimostra che dato un dominio limitato strettamente convesso \( \Omega \) in \( C^{n} \) con bordo analitico reale e un punto \( x_{0} \) in \( \Omega \), esiste un dominio limitato strettamente convesso \( \Omega ' \) con bordo analitico reale contenente \( \Omega \) ma vicino ad esso quanto si vuole, tale che \( \Omega \) è una palla per la distanza di Kobayashi di \( \Omega ' \) con centro in \( x_{0} \). Come applicazione si dimostra che se \( \Omega \) non è biolomorfo alla palla, allora ogni suo automorfismo si estende a un automorfismo di \( \Omega ' \). 
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     title = {Balls for the {Kobayashi} distance and extension of the automorphisms of strictly convex domains in \( {C^{n}} \) with real analytic boundary},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
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Iannuzzi, Andrea. Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in \( C^{n} \) with real analytic boundary. Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 5 (1994) no. 2, pp. 193-196. http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_2_a9/

[1] M. Abate, Iteration theory of holomorphic maps on taut manifolds. Mediterranean Press, 1989. | MR | Zbl

[2] E. Bedford - D. Burns, Holomorphic mapping of annuli in \( C^{n} \) and the associated extremal function. Ann. Scuola Norm. Sup. Pisa, Serie IV, 6, 1979, 381-414. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[3] J. Bland - T. Duchamp - M. Kalka, On the automorphism group of strictly convex domains in \( C^{n} \). A.M.S., Providence 1986 Contemp. Math., 49, 19-30. | DOI | MR | Zbl

[4] E. Bedford - A. Taylor, The Dirichlet problem for a complex Monge-Ampère equation. Inv. Math., 37, 1976, 1-44. | fulltext EuDML | MR | Zbl

[5] L. Lempert, La métrique de Kobayashi et la representation des domaines sur la boule. Bull. Soc. Math. France, 109, 1981, 427-474. | fulltext EuDML | fulltext mini-dml | MR | Zbl

[6] L. Lempert, Solving the degenerate Monge-Ampère equation with a concentrated singularity. Math. Ann., 263, 1983, 515-532. | fulltext EuDML | DOI | MR | Zbl

[7] G. Patrizio, Parabolic exhaustions for strictly convex domains. Manuscripta Math., 47, 1984, 271-309. | fulltext EuDML | DOI | MR | Zbl

[8] A. G. Vitushkin, Holomorphic extensions of mappings of compact hypersurfaces. Math. USSR Izvestiya, 20, 1983, 27-33. | MR | Zbl

[9] P. M. Wong, On umbilical hypersurfaces and uniformization of circular domains. Proc. Symposia Pure Math. AMS, vol. 41, 1984, 225-252. | MR | Zbl