Inequalities for the curvature of curves and surfaces

D. Cohen Steiner, H. Edelsbrunner, Foundations of Computational Mathematics 7 (2007) 391–404.

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Abstract
In this paper we bound the difference between the total mean curvatures of two closed surfaces in 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.
Publishing Year
Date Published
2007-11-01
Journal Title
Foundations of Computational Mathematics
Volume
7
Issue
4
Page
391 - 404
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Cohen Steiner D, Edelsbrunner H. Inequalities for the curvature of curves and surfaces. Foundations of Computational Mathematics. 2007;7(4):391-404. doi:10.1007/s10208-005-0200-3
Cohen Steiner, D., & Edelsbrunner, H. (2007). Inequalities for the curvature of curves and surfaces. Foundations of Computational Mathematics, 7(4), 391–404. https://doi.org/10.1007/s10208-005-0200-3
Cohen Steiner, David, and Herbert Edelsbrunner. “Inequalities for the Curvature of Curves and Surfaces.” Foundations of Computational Mathematics 7, no. 4 (2007): 391–404. https://doi.org/10.1007/s10208-005-0200-3.
D. Cohen Steiner and H. Edelsbrunner, “Inequalities for the curvature of curves and surfaces,” Foundations of Computational Mathematics, vol. 7, no. 4, pp. 391–404, 2007.
Cohen Steiner D, Edelsbrunner H. 2007. Inequalities for the curvature of curves and surfaces. Foundations of Computational Mathematics. 7(4), 391–404.
Cohen Steiner, David, and Herbert Edelsbrunner. “Inequalities for the Curvature of Curves and Surfaces.” Foundations of Computational Mathematics, vol. 7, no. 4, Springer, 2007, pp. 391–404, doi:10.1007/s10208-005-0200-3.

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