Geodesic
Remarks on Chebyshev coordinates
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 5-13

Voir la notice de l'article provenant de la source Math-Net.Ru

Some results on the existence of global Chebyshev coordinates on complete Riemannian manifolds or, more generally, on Aleksandrov surfaces are proved. For instance, if both the positive part and the negative part of the integral curvature are less than $2\pi$, then there exist global Chebyshev coordinates on $M$. Such coordinates help one to get bi-Lipschitz maps between surfaces. 
@article{ZNSL_2005_329_a0,
     author = {Yu. D. Burago and S. V. Ivanov and S. G. Malev},
     title = {Remarks on {Chebyshev} coordinates},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {5--13},
     publisher = {mathdoc},
     volume = {329},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a0/}
}
TY  - JOUR
AU  - Yu. D. Burago
AU  - S. V. Ivanov
AU  - S. G. Malev
TI  - Remarks on Chebyshev coordinates
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2005
SP  - 5
EP  - 13
VL  - 329
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a0/
LA  - ru
ID  - ZNSL_2005_329_a0
ER  - 
%0 Journal Article
%A Yu. D. Burago
%A S. V. Ivanov
%A S. G. Malev
%T Remarks on Chebyshev coordinates
%J Zapiski Nauchnykh Seminarov POMI
%D 2005
%P 5-13
%V 329
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a0/
%G ru
%F ZNSL_2005_329_a0
Yu. D. Burago; S. V. Ivanov; S. G. Malev. Remarks on Chebyshev coordinates. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 9, Tome 329 (2005), pp. 5-13. http://geodesic.mathdoc.fr/item/ZNSL_2005_329_a0/