Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in C n with real analytic boundary

Andrea Iannuzzi

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 2, page 193-196
  • ISSN: 1120-6330

Abstract

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It is shown that given a bounded strictly convex domain Ω in C n with real analitic boundary and a point x 0 in Ω , there exists a larger bounded strictly convex domain Ω ′ with real analitic boundary, close as wished to Ω , such that Ω is a ball for the Kobayashi distance of Ω ′ with center x 0 . The result is applied to prove that if Ω is not biholomorphic to the ball then any automorphism of Ω extends to an automorphism of Ω ′ .

How to cite

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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. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.2 (1994): 193-196. <http://eudml.org/doc/244172>.

@article{Iannuzzi1994,
abstract = {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 \( \Omega ' \).},
author = {Iannuzzi, Andrea},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Kobayashi distance; Automorphisms of bounded domains; Complex Monge Ampère equation; extension; automorphisms; strictly convex domains; real analytic boundary; Kobayashi ball},
language = {eng},
month = {6},
number = {2},
pages = {193-196},
publisher = {Accademia Nazionale dei Lincei},
title = {Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in \( C^\{n\} \) with real analytic boundary},
url = {http://eudml.org/doc/244172},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Iannuzzi, Andrea
TI - Balls for the Kobayashi distance and extension of the automorphisms of strictly convex domains in \( C^{n} \) with real analytic boundary
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/6//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 2
SP - 193
EP - 196
AB - 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 \( \Omega ' \).
LA - eng
KW - Kobayashi distance; Automorphisms of bounded domains; Complex Monge Ampère equation; extension; automorphisms; strictly convex domains; real analytic boundary; Kobayashi ball
UR - http://eudml.org/doc/244172
ER -

References

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  1. ABATE, M., Iteration theory of holomorphic maps on taut manifolds. Mediterranean Press, 1989. Zbl0747.32002MR1098711
  2. BEDFORD, E. - BURNS, D., Holomorphic mapping of annuli in C n and the associated extremal function. Ann. Scuola Norm. Sup. Pisa, Serie IV, 6, 1979, 381-414. Zbl0422.32021MR553791
  3. BLAND, J. - DUCHAMP, T. - KALKA, M., On the automorphism group of strictly convex domains in C n . A.M.S., Providence1986Contemp. Math., 49, 19-30. Zbl0589.32050MR833801DOI10.1090/conm/049/833801
  4. BEDFORD, E. - TAYLOR, A., The Dirichlet problem for a complex Monge-Ampère equation. Inv. Math., 37, 1976, 1-44. Zbl0315.31007MR445006
  5. LEMPERT, L., La métrique de Kobayashi et la representation des domaines sur la boule. Bull. Soc. Math. France, 109, 1981, 427-474. Zbl0492.32025MR660145
  6. LEMPERT, L., Solving the degenerate Monge-Ampère equation with a concentrated singularity. Math. Ann., 263, 1983, 515-532. Zbl0531.35020MR707246DOI10.1007/BF01457058
  7. PATRIZIO, G., Parabolic exhaustions for strictly convex domains. Manuscripta Math., 47, 1984, 271-309. Zbl0581.32018MR744324DOI10.1007/BF01174598
  8. VITUSHKIN, A. G., Holomorphic extensions of mappings of compact hypersurfaces. Math. USSR Izvestiya, 20, 1983, 27-33. Zbl0571.32011MR643891
  9. WONG, P. M., On umbilical hypersurfaces and uniformization of circular domains. Proc. Symposia Pure Math.AMS, vol. 41, 1984, 225-252. Zbl0587.32029MR740886

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