Extreme properties of curves with bounded curvature on a sphere
  We give a sharp lower bound on the area of the domain enclosed by an embedded curve lying on a two-dimensional sphere, provided that geodesic curvature of this curve is bounded from below. Furthermore, we prove some dual inequalities for convex curves whose curvatures are bounded from above. 
Alexander Borisenko, Kostiantyn Drach
math.DG math.OC