Geodesic
Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature
Archivum mathematicum, Tome 50 (2014) no. 4, pp. 219-236.

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We relate the total curvature and the isoperimetric deficit of a curve $\gamma $ in a two-dimensional space of constant curvature with the area enclosed by the evolute of $\gamma $. We provide also a Gauss-Bonnet theorem for a special class of evolutes.
DOI : 10.5817/AM2014-4-219
Classification : 52A10, 52A55, 53A04
Keywords: curvature; evolutes; isoperimetric deficit; Gauss-Bonnet 
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     title = {Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature},
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Cufí, Julià; Reventós, Agustí. Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature. Archivum mathematicum, Tome 50 (2014) no. 4, pp. 219-236. doi : 10.5817/AM2014-4-219. http://geodesic.mathdoc.fr/articles/10.5817/AM2014-4-219/

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