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arXiv · 1402.2691

Comparison theorem for support functions of hypersurfaces

Alexander Borisenko·Kostiantyn Drach
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Abstract

For a convex domain $D$ that is enclosed by the hypersurface $\partial D$ of bounded normal curvature, we prove an angle comparison theorem for angles between $\partial D$ and geodesic rays starting from some fixed point in $D$, and the corresponding angles for hypersurfaces of constant normal curvature. Also, we obtain a comparison theorem for support functions of such surfaces. As a corollary, we present a proof of Blaschke's Rolling Theorem.

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Alexander Borisenko, Kostiantyn Drach. 2014-02-11. Comparison theorem for support functions of hypersurfaces. https://arxiv.org/abs/1402.2691

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