Evolutes and isoperimetric deficit in two-dimensional spaces of constant   curvature
  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. 
Juli\`a Cuf\'i and Agust\'i Revent\'os
math.DG