Comparison theorem for the support functions of hypersurfaces
DOI:
https://doi.org/10.15407/dopovidi2015.03.011Keywords:
Blaschke’s rolling theorem, hypersurface, support functionsAbstract
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.
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