A complete 3-dimensional Blaschke-Santaló diagram

2014/04/27 by Brandenberg, René, Merino, Bernardo González · 2 citations
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1404.6808

Abstract

We present a complete 3-dimensional Blaschke-Santaló diagram for planar convex bodies with respect to the four classical magnitudes inner and outer radius, diameter and (minimal) width in euclidean spaces.

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• Bounding the diameter-width ratio using containment inequalities of means of convex bodies
• A complete system of inequalities for the diameter, in-, and circumradius in the 3-dimensional Euclidean space

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