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A minimax inequality for inscribed cones revisited

Part of: General convexity

Published online by Cambridge University Press:  31 August 2023

Zokhrab Mustafaev
Zokhrab Mustafaev*
Affiliation:
Department of Mathematics, University of Houston–Clear Lake, Houston, TX 77058, USA
*
e-mail: mustafaev@uhcl.edu
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Abstract

In 1993, E. Lutwak established a minimax inequality for inscribed cones of origin symmetric convex bodies. In this work, we re-prove Lutwak’s result using a maxmin inequality for circumscribed cylinders. Furthermore, we explore connections between the maximum volume of inscribed double cones of a centered convex body and the minimum volume of circumscribed cylinders of its polar body.

Keywords

Blaschke–Santaló inequalitycircumscribed cylindercross-sectional measuresinscribed coneisoperimetrixprojection body

MSC classification

Primary: 52A20: Convex sets in $n$ dimensions (including convex hypersurfaces)
Secondary: 52A40: Inequalities and extremum problems
Type
Article
Information
Canadian Mathematical Bulletin , Volume 67 , Issue 1 , March 2024 , pp. 215 - 221
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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