naa a22 4500 510810462 CHVBK 20180411083440.0 cr unu---uuuuu 180411e20130101xx s 000 0 eng 10.1007/s12220-011-9262-4 doi (NATIONALLICENCE)springer-10.1007/s12220-011-9262-4 Lipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces [Elektronische Daten] [U. Boscain, G. Charlot, R. Ghezzi, M. Sigalotti] Two-dimensional almost-Riemannian structures are generalized Riemannian structures on surfaces for which a local orthonormal frame is given by a Lie bracket generating pair of vector fields that can become collinear. We consider the Carnot-Carathéodory distance canonically associated with an almost-Riemannian structure and study the problem of Lipschitz equivalence between two such distances on the same compact oriented surface. We analyze the generic case, allowing in particular for the presence of tangency points, i.e., points where two generators of the distribution and their Lie bracket are linearly dependent. The main result of the paper provides a characterization of the Lipschitz equivalence class of an almost-Riemannian distance in terms of a labeled graph associated with it. Mathematica Josephina, Inc., 2011 Almost-Riemannian surface nationallicence Lipschitz equivalence nationallicence Carnot-Carathéodory distance nationallicence Sub-Riemannian geometry nationallicence Boscain U. CNRS CMAP & Team INRIA GECO, École Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France aut Charlot G. Institut Fourier & Team INRIA GECO, UMR 5582, CNRS/Université Grenoble 1, 100 rue des Maths, BP 74, 38402, St Martin d'Hères, France aut Ghezzi R. CMAP & Team INRIA GECO, École Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France aut Sigalotti M. Team INRIA GECO, INRIA Saclay-Île-de-France, Parc Orsay Université, 4 rue Jacques Monod, 91893, Orsay Cedex, France aut Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 438-455 1050-6926 23:1<438 2013 23 12220 https://doi.org/10.1007/s12220-011-9262-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s12220-011-9262-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Boscain U. CNRS CMAP & Team INRIA GECO, École Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France aut NATIONALLICENCE 700 1- Charlot G. Institut Fourier & Team INRIA GECO, UMR 5582, CNRS/Université Grenoble 1, 100 rue des Maths, BP 74, 38402, St Martin d'Hères, France aut NATIONALLICENCE 700 1- Ghezzi R. CMAP & Team INRIA GECO, École Polytechnique Route de Saclay, 91128, Palaiseau Cedex, France aut NATIONALLICENCE 700 1- Sigalotti M. Team INRIA GECO, INRIA Saclay-Île-de-France, Parc Orsay Université, 4 rue Jacques Monod, 91893, Orsay Cedex, France aut NATIONALLICENCE 773 0- Journal of Geometric Analysis Springer-Verlag 23/1(2013-01-01), 438-455 1050-6926 23:1<438 2013 23 12220 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer