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 \( \Omega ' \). 
@article{RLIN_1994_9_5_2_a9,
     author = {Iannuzzi, Andrea},
     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},
     pages = {193--196},
     publisher = {mathdoc},
     volume = {Ser. 9, 5},
     number = {2},
     year = {1994},
     zbl = {0807.32020},
     mrnumber = {MR1292575},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1994_9_5_2_a9/}
}
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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/