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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Isometries for the Carathéodory metric


Authors: Marco Abate and Jean-Pierre Vigué
Journal: Proc. Amer. Math. Soc. 136 (2008), 3905-3909
MSC (2000): Primary 32H02
Published electronically: May 20, 2008
MathSciNet review: 2425730
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Abstract: Given two open unit balls $ B_1$ and $ B_2$ in complex Banach spaces, we consider a holomorphic mapping $ f\colon B_1\to B_2$ such that $ f(0)=0$ and $ f'(0)$ is an isometry. Under some additional hypotheses on the Banach spaces involved, we prove that $ f(B_1)$ is a complex closed analytic submanifold of $ B_2$.


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Additional Information

Marco Abate
Affiliation: Dipartimento di Matematica, Università di Pisa, Largo Pontecorvo 5, 56127 Pisa, Italy
Email: abate@dm.unipi.it

Jean-Pierre Vigué
Affiliation: LMA, Université de Poitiers, CNRS, Mathématiques, SP2MI, BP 30179, 86962 Futuroscope cedex, France
Email: vigue@math.univ-poitiers.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09391-X
PII: S 0002-9939(08)09391-X
Received by editor(s): July 17, 2007
Received by editor(s) in revised form: September 19, 2007
Published electronically: May 20, 2008
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2008 American Mathematical Society