Per citar aquest document: http://ddd.uab.cat/record/118294
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

DOI: 10.5565/PUBLMAT_Extra14_04


17 p, 1.8 MB

El registre apareix a les col·leccions:
Articles > Articles publicats > Publicacions matemàtiques
Articles > Articles de recerca

 Registre creat el 2014-05-19, darrera modificació el 2016-06-04



   Favorit i Compartir