Comparison theorem for the support functions of hypersurfaces

Authors

  • A.A. Borisenko
  • K.D. Drach

DOI:

https://doi.org/10.15407/dopovidi2015.03.011

Keywords:

Blaschke’s rolling theorem, hypersurface, support functions

Abstract

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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Published

21.01.2025

How to Cite

Borisenko, A., & Drach, K. (2025). Comparison theorem for the support functions of hypersurfaces . Reports of the National Academy of Sciences of Ukraine, (3), 11–16. https://doi.org/10.15407/dopovidi2015.03.011