The Surface Area Deviation of the Euclidean Ball and a Polytope

2015/10/31 by Steven Hoehner, Steven D. Hoehner, Carsten Schütt +2 · 13 citations
Computer Science · Mathematics · #Ball (mathematics) #Combinatorics #Computational Geometry and Mesh Generation #Convex body #Convex hull #Convex optimization #Convex polytope #Convex set #Euclidean geometry #Geometry #Inscribed figure #Mathematics #Point processes and geometric inequalities #Polytope #Regular polygon #Surface (topology) #math.PR

paper · pdf · doi:10.1007/s10959-016-0701-9

published in Journal of Theoretical Probability 31(1), 244-267 (Springer Science+Business Media)

arxiv created 2016/06/27 · openalex publication_date 2016/07/11 · openalex created_date 2019/06/27 · arxiv updated 2021/03/03 · openalex updated_date 2026/08/05

Abstract

While there is extensive literature on approximation of convex bodies by inscribed or circumscribed polytopes, much less is known in the case of generally positioned polytopes. Here we give upper and lower bounds for approximation of convex bodies by arbitrarily positioned polytopes with a fixed number of vertices in the symmetric surface area deviation.

Citations

• Convex and Discrete Geometry
• Geometric Measure Theory

Cited by

• Intrinsic and Dual Volume Deviations of Convex Bodies and Polytopes