Remarks on Chebyshev coordinates
  Some 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 2\pi each, then there exist global Chebyshev coordinates on M. These conditions are optimal. Such coordinates help to get bi-Lipschitz maps between surfaces.} 
Yu. Burago, S. Ivanov, and S. Malev