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arXiv:1403.3236 [math.DG]AbstractReferencesReviewsResources

Evolutes and isoperimetric deficit in two-dimensional spaces of constant curvature

Julià Cufí, Agustí Reventós

Published 2014-03-13Version 1

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.

Comments: 16 pages, 3 figures
Categories: math.DG
Subjects: 53A04
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