Skip to Main Content

Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Isometries for the Carathéodory metric
HTML articles powered by AMS MathViewer

by Marco Abate and Jean-Pierre Vigué PDF
Proc. Amer. Math. Soc. 136 (2008), 3905-3909 Request permission

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 $B_2$.
References
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32H02
  • Retrieve articles in all journals with MSC (2000): 32H02
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
  • 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
  • © Copyright 2008 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3905-3909
  • MSC (2000): Primary 32H02
  • DOI: https://doi.org/10.1090/S0002-9939-08-09391-X
  • MathSciNet review: 2425730