Comparison theorem for the support functions of hypersurfaces - Borisenko, A.A.; Drach, K.D. (Reports of the National Academy of Sciences of Ukraine, 2015)
For a convex domain D that is enclosed by the hypersurface ∂D of bounded normal curvature, we prove an angle comparison theorem for the angles between ∂D and geodesic rays starting from some fixed point in D, and the corresponding angles for hypersurfaces of constant normal curvature. We obtain a comparison theorem for the support functions of such surfaces. As a corollary, we present a proof of Blaschke’s rolling theorem.