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

Data: 2014
Resum: 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.
Drets: Tots els drets reservats
Llengua: Anglès
Document: article ; recerca ; publishedVersion
Matèria: Half-Reeb components ; Foliations ; Palais-Smale conditions ; Global injectivity
Publicat a: Publicacions matemàtiques, Vol. Extra, Núm. (2014) , p. 63-79, ISSN 0214-1493

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_Extra14_04
DOI: 10.5565/PUBLMAT_Extra14_04
DOI: 10.5565/287200

17 p, 1.8 MB

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