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Local homeo- and diffeomorphisms: invertibility and convex image

Published online by Cambridge University Press:  17 April 2009

Gaetano Zampieri  and
Gianluca Gorni
Gaetano Zampieri
Affiliation:
Dipartimento di Matematica Pura eApplicata Università di Padovavia Belzoni 7 35131 PadovaItaly e-mail: gaentano@pdmat1.unipd.it
Gianluca Gorni
Affiliation:
Dipartimento di Matematica eInformatica Università di Udinevia Zanon 6 33100 UdineItaly e-mail: gorni@udmi5400.cineca.it
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We prove a necessary and sufficient condition for a local homeomorphism defined on an open, connected subset of a Euclidean space to be globally one-to-one and, at the same time, for the image to be convex. Among the applications we give a practical sufficiency test for invertibility for twice differentiable local diffeomorphisms defined on a ball.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 49 , Issue 3 , June 1994 , pp. 377 - 398
Copyright
Copyright © Australian Mathematical Society 1994

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