{"publisher":"Springer","intvolume":" 7","status":"public","title":"Inequalities for the curvature of curves and surfaces","publication_status":"published","_id":"3973","year":"2007","volume":7,"date_created":"2018-12-11T12:06:12Z","date_updated":"2021-01-12T07:53:34Z","author":[{"full_name":"Cohen-Steiner, David","first_name":"David","last_name":"Cohen Steiner"},{"full_name":"Herbert Edelsbrunner","first_name":"Herbert","last_name":"Edelsbrunner","id":"3FB178DA-F248-11E8-B48F-1D18A9856A87","orcid":"0000-0002-9823-6833"}],"type":"journal_article","extern":1,"publist_id":"2154","issue":"4","abstract":[{"lang":"eng","text":"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."}],"page":"391 - 404","quality_controlled":0,"citation":{"ama":"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","ista":"Cohen Steiner D, Edelsbrunner H. 2007. Inequalities for the curvature of curves and surfaces. Foundations of Computational Mathematics. 7(4), 391–404.","ieee":"D. Cohen Steiner and H. Edelsbrunner, “Inequalities for the curvature of curves and surfaces,” Foundations of Computational Mathematics, vol. 7, no. 4. Springer, pp. 391–404, 2007.","apa":"Cohen Steiner, D., & Edelsbrunner, H. (2007). Inequalities for the curvature of curves and surfaces. Foundations of Computational Mathematics. Springer. https://doi.org/10.1007/s10208-005-0200-3","mla":"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.","short":"D. Cohen Steiner, H. Edelsbrunner, Foundations of Computational Mathematics 7 (2007) 391–404.","chicago":"Cohen Steiner, David, and Herbert Edelsbrunner. “Inequalities for the Curvature of Curves and Surfaces.” Foundations of Computational Mathematics. Springer, 2007. https://doi.org/10.1007/s10208-005-0200-3."},"publication":"Foundations of Computational Mathematics","date_published":"2007-11-01T00:00:00Z","doi":"10.1007/s10208-005-0200-3","day":"01","month":"11"}