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Inequalities for the Curvature of Curves and Surfaces

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Abstract

In this paper we bound the difference between the total mean curvatures of two closed surfaces in \({\Bbb R}^3\) in terms of their total absolute curvatures and the Frechet distance between the volumes they enclose. The proof relies on a combination of methods from algebraic topology and integral geometry. We also bound the difference between the lengths of two curves using the same methods.

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Authors and Affiliations

  1. Projet Geometrica, INRIA, Sophia-Antipolis, France

    Cohen-Steiner Narcowich

  2. Department of Computer Science and Mathematics, Duke University, Durham, North Carolina and Geomagic, Research Triangle Park, North Carolina, USA

    Herbert Edelsbrunner

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  1. Cohen-Steiner Narcowich
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  2. Herbert Edelsbrunner
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Narcowich, CS., Edelsbrunner, H. Inequalities for the Curvature of Curves and Surfaces. Found Comput Math 7, 391–404 (2007). https://doi.org/10.1007/s10208-005-0200-3

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  • DOI: https://doi.org/10.1007/s10208-005-0200-3

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