Farthest points and cut loci on some degenerate convex surfaces

Criteria for farthest points on convex s

Criteria for farthest points on convex surfaces

✍ Jin-ichi Itoh; Costin Vǐlcu 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 211 KB

## Abstract We provide a sharp, sufficient condition to decide if a point __y__ on a convex surface __S__ is a farthest point (i.e., is at maximal intrinsic distance from some point) on __S__, involving a lower bound __π__ on the total curvature __ω~y~__ at __y__, __ω~y~__ ≥ __π__. Further conseque