Half-Reeb components, Palais-Smale condition and global injectivity of local diffeomorphisms in R3
Braun, Francisco (Universidade Federal de São Carlos. Departamento de Matemática)
Venato-Santos, Jean (Universidade Federal de Uberlândia. Faculdade de Matemática)

Date:	2014
Abstract:	Let F = (F1, F2, F3): R3 → R3 be a C∞ local diffeomorphism. We prove that each of the following conditions are sufficient to the global injectivity of F: A) The foliations FFi made up by the connected components of the level surfaces Fi = constant, consist of leaves without half-Reeb components induced by Fj , j ∈ {1, 2, 3} \ {i}, for i ∈ {1, 2, 3}. B) For each i 6= j ∈ {1, 2, 3}, Fi $l : L → R satisfy the Palais-Smale condition, for all L ∈ FFj. We also prove that B) implies A) and give examples to show that the converse is not true. Further, we give examples showing that none of these conditions is necessary to the global injectivity of F.
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Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Half-Reeb components ; Foliations ; Palais-Smale conditions ; Global injectivity
Published in:	Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 63-79, ISSN 2014-4350

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/287200
DOI: 10.5565/PUBLMAT_Extra14_04

17 p, 1.8 MB

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