Geometriae Dedicata

, Volume 67, Issue 1, pp 1–30

Convexity and the Average Curvature of Plane Curves

  • Jefferey C. Lagarias
  • Thomas J. Richardson
Article

DOI: 10.1023/A:1004912521664

Cite this article as:
Lagarias, J.C. & Richardson, T.J. Geometriae Dedicata (1997) 67: 1. doi:10.1023/A:1004912521664

Abstract

The average curvature of a rectifiable closed curve in R2 is its total absolute curvature divided by its length. If a rectifiable closed curve in R2 is contained in the interior of a convex set D then its average curvature is at least as large as the average curvature of the simple closed curve ∂ D which bounds the convex set.

Average curvature total curvature convexity integral geometry plane curve geometric inequalities. 

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Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Jefferey C. Lagarias
    • 1
  • Thomas J. Richardson
    • 2
  1. 1.AT & T Labs–ResearchFlorham ParkU.S.A.
  2. 2.Bell LaboratoriesMurray HillU.S.A.

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