On the localization principle for the automorphisms of pseudoellipsoids

Authors:
Mario Landucci and Andrea Spiro

Journal:
Proc. Amer. Math. Soc. **137** (2009), 1339-1345

MSC (2000):
Primary 32H12, 32H02, 32H35

DOI:
https://doi.org/10.1090/S0002-9939-08-09726-8

Published electronically:
December 3, 2008

MathSciNet review:
2465657

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that Alexander's extendibility theorem for a local automorphism of the unit ball is valid also for a local automorphism of a pseudoellipsoid , provided that is defined on a region such that: i) contains an open set of strongly pseudoconvex points; ii) for any . By the counterexamples we exhibit, such hypotheses can be considered as optimal.

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Additional Information

**Mario Landucci**

Affiliation:
Dip. Matematica Applicata “G. Sansone”, Università di Firenze, Via di Santa Marta 3, I-50139 Firenze, Italy

Email:
mario.landucci@unifi.it

**Andrea Spiro**

Affiliation:
Dip. Matematica e Informatica, Università di Camerino, Via Madonna delle Carceri, I-62032 Camerino (Macerata), Italy

Email:
andrea.spiro@unicam.it

DOI:
https://doi.org/10.1090/S0002-9939-08-09726-8

Keywords:
Alexander theorem,
pseudoellipsoids,
localization principle

Received by editor(s):
June 25, 2007

Received by editor(s) in revised form:
February 17, 2008

Published electronically:
December 3, 2008

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.