2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102078Some results on existence of global Chebyshev coordinates on a Riemannian manifold or, more generally, on Aleksandrov surface are proved. For instance, if the positive and the negative parts of integral curvature of a Riemannian manifold M are less than 2πeach, then there exist global Chebyshev coordinates on M. These conditions are optimal. Such coordinates help to get bi-Lipschitz maps between surfaces.}This is a corrected version of our previous submissonDifferential GeometryMetric Geometry53Ctext