01360nas a2200181   4500008004100000022001400041245008900055210006900144260000800213300001400221490000700235520080900242100001701051700002301068700002001091700002101111856004601132       2013                        eng d  a1559-002X00aLipschitz Classification of Almost-Riemannian Distances on Compact Oriented Surfaces0 aLipschitz Classification of AlmostRiemannian Distances on Compac  cJan  a438–4550 v233 a<p>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.</p>1 aBoscain, Ugo1 aCharlot, Grégoire1 aGhezzi, Roberta1 aSigalotti, Mario  uhttps://doi.org/10.1007/s12220-011-9262-4