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Global inversion and covering maps on length spaces


Garrido, M. Isabel and Gutú, Olivia and Jaramillo Aguado, Jesús Ángel (2010) Global inversion and covering maps on length spaces. Nonlinear Analysis-Theory Methods & Applications, 73 (5). pp. 1364-1374. ISSN 0362-546X

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In order to obtain global inversion theorems for mappings between length metric spaces, we investigate sufficient conditions for a local homeomorphism to be a covering map in this context. We also provide an estimate of the domain of invertibility of a local homeomorphism around a point, in terms of a kind of lower scalar derivative. As a consequence, we obtain an invertibility result using an analog of the Hadamard integral condition in the frame of length spaces. Some applications are given to the case of local diffeomorphisms between Banach-Finsler manifolds. Finally, we derive a global inversion theorem for mappings between stratified groups.

Item Type:Article
Uncontrolled Keywords:Global inversion; Length spaces; Coverings maps; Banach-Finsler manifolds
Subjects:Sciences > Mathematics > Mathematical analysis
ID Code:16215

J. Hadamard, Sur les transformations ponctuelles, Bull. Soc. Math. France 34 (1906) 71-84.

P. Lévy, Sur les fonctions des lignes implicites, Bull. Soc. Math. France 48 (1920) 13-27.

F. John, On quasi-isometric maps I, Comm. Pure Appl. Math. 21 (1968) 77-110.

R. Plastock, Homeomorphisms between Banach spaces, Trans. Amer. Math. Soc. 200 (1974) 169-183.

P. Rabier, On global diffeomorphisms of Euclidean space, Nonlinear Anal. 21 (1993) 925-947.

P. Rabier, Ehresmann fibrations and Palais_Smale Conditions for morphism of finsler manifolds, Ann. of Math. 146 (1997) 547-691.

S. Nollet, F. Xavier, Global inversion via the Palais_Smale condition, Discrete Contin. Dyn. Syst. 8 (2002) 17-28.

[G. Katriel, Mountain-pass theorems and global homeomorphism theorems, Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994) 189-209.

O. Gutú, J.A. Jaramillo, Global homeomorphisms and covering projections on metric spaces, Math. Ann. 338 (2007) 75-95.

O. Gutú, Global inversion theorems via coercive functionals on metric spaces, Nonlinear Anal. 66 (2007) 2688-2697.

F.E. Browder, Covering spaces, fiber spaces and local homeomorphism, Duke Math. J. 21 (1954) 329-336.

A. Hatcher, Algebraic Topology, Cambridge University Press, 2002.

K.H. Neeb, A Cartan_Hadamard theorem for Banach_Finsler manifolds, Geom. Dedicata 95 (2002) 115-156.

H. Upmeier, Symmetric Banach manifolds and Jordan c_-algebras, North-Holland Math. Stud. 104 (1985).

R.S. Palais, Lusternik_Schnirelman theory on Banach manifolds, Topology 5 (1966) 115-132.

B. Josefson, Weak sequential convergence in the dual of a Banach space does not imply norm convergence, Ark. Mat. 13 (1975) 79-89.

A. Nissenzweig, w_ sequential convergence, Israel J. Math. 22 (1975) 266-272.

S. Lang, Fundamentals of Differential Geometry, in: GTM, vol. 191, Springer-Verlag, 1999.

N. Arcozzi, D. Morbidelli, A global inverse map theorem and bi-lipschitz maps in the heisenberg group, Annali dell Universitá di Ferrara 52 (2006) 189-197.

G.B. Folland, E. Stein, Hardy Spaces on Homogeneous Groups, Princeton University Press, 1982.

M. Gromov, Carnot_Carathéodory spaces seen from within, in: Subriemannian Geometry, in: A. Bellaïche, J. Risler (Eds.), Progress in Math., vol. 144, Verlag, Birkhauser, 1996.

V. Magnani, Elements of Geometric Measure Theory on Sub-Riemannian groups, Ph.D. Thesis of Scuola Normale Superiore de Pisa, 2002.

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