On the reverse Orlicz Blaschke-Santaló inequality (Q1635721)
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scientific article; zbMATH DE number 6879872
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the reverse Orlicz Blaschke-Santaló inequality |
scientific article; zbMATH DE number 6879872 |
Statements
On the reverse Orlicz Blaschke-Santaló inequality (English)
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1 June 2018
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In this paper the author deals with a family of isoperimetric inequalities which compare the volume of a convex body with that of its Orlicz centroid body defined by \textit{E. Lutwak} et al. [J. Differ. Geom. 84, No. 2, 365--387 (2010; Zbl 1206.49050)]. In particular, he also addresses the question of a reverse Orlicz Blaschke-Santaló inequality and establishes such an inequality in the two-dimensional case. The extremality of triangles is derived, and the restriction to centrally symmetric convex figures yields parallelograms as extremal figures. Further on, a nice characterization of ellipsoids in the studied framework is obtained.
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Orlicz centroid body
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reverse Orlicz Blaschke-Santaló inequality
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shadow systems
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parallel chord movement
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isoperimetric inequalities
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volume
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convex body
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ellipsoids
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