Comparison theorem for the support functions of hypersurfaces

TitleComparison theorem for the support functions of hypersurfaces
Publication TypeJournal Article
Year of Publication2015
AuthorsBorisenko, AA, Drach, KD
Abbreviated Key TitleDopov. Nac. akad. nauk Ukr.
DOI10.15407/dopovidi2015.03.011
Issue3
SectionMathematics
Pagination11-16
Date Published3/2015
LanguageRussian
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 the angles between $\partial D$ 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.
KeywordsBlaschke’s rolling theorem, hypersurface, support functions
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