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arXiv · 2309.07772

Narrowing the gaps of the missing Blaschke-Santal\'o diagrams

Bernardo González Merino
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Abstract

We solve several new sharp inequalities relating three quantities amongst the area, perimeter, inradius, circumradius, diameter, and minimal width of planar convex bodies. As a consequence, we narrow the missing gaps in each of the missing planar Blaschke-Santal\'o diagrams. Furthermore, we extend some of those sharp inequalities into higher dimensions, by replacing either the perimeter by the mean width or the area by the volume.

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Bernardo González Merino. 2023-09-14. Narrowing the gaps of the missing Blaschke-Santal\'o diagrams. https://arxiv.org/abs/2309.07772

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