Troyanov, Marc2007-12-172007-12-172007-12-17199010.5802/aif.1241https://infoscience.epfl.ch/handle/20.500.14299/15757We study conditions under which a point of a Riemannian surface has a neighborhood that can be parametrized by polar coordinates. The point under investigation can be a regular point or a conical singularity. We also study the regularity of these polar coordinates in relation with the regularity of the curvature.text::journal::journal article::research article