Coordonnées polaires sur les surfaces riemanniennes singulières
Annales de l'Institut Fourier, Tome 40 (1990) no. 4, p. 913-937
Nous étudions les conditions sous lesquelles un point d’une surface riemannienne possède un voisinage pouvant être paramétrisé par des coordonnées polaires. Le point en question peut être un point régulier ou un point singulier conique. Nous étudions aussi la régularité de ces coordonnées polaires en fonction de la régularité de la courbure.
We 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.
@article{AIF_1990__40_4_913_0,
     author = {Troyanov, Marc},
     title = {Coordonn\'ees polaires sur les surfaces riemanniennes singuli\`eres},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Durand},
     address = {28 - Luisant},
     volume = {40},
     number = {4},
     year = {1990},
     pages = {913-937},
     doi = {10.5802/aif.1241},
     mrnumber = {1096597},
     zbl = {0711.53017},
     mrnumber = {92d:30029},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1990__40_4_913_0}
}
Troyanov, Marc. Coordonnées polaires sur les surfaces riemanniennes singulières. Annales de l'Institut Fourier, Tome 40 (1990) no. 4, pp. 913-937. doi : 10.5802/aif.1241. http://www.numdam.org/item/AIF_1990__40_4_913_0/

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