This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the Lp-centroid body, and theyr polars. Examples are the Blaschke-Santalò inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodies provides a general approach to this subject. A family of inequalities, depending on a parameter p and proved by Lutwak for p=1 and p=2 , is obtained.
Campi, S., Gronchi, P. (2006). Volume inequalities for sets associated with convex bodies. In Integral Geometry and Convexity (pp.1-16). World Scientific Publishing Co. Pte. Ltd., Singapore.
Volume inequalities for sets associated with convex bodies
CAMPI, STEFANO;
2006-01-01
Abstract
This paper deals with inequalities for the volume of a convex body and the volume of the projection body, the Lp-centroid body, and theyr polars. Examples are the Blaschke-Santalò inequality, the Petty and Zhang projection inequalities, the Busemann-Petty inequality. Other inequalities of the same type are still at the stage of conjectures. The use of special continuous movements of convex bodies provides a general approach to this subject. A family of inequalities, depending on a parameter p and proved by Lutwak for p=1 and p=2 , is obtained.
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https://hdl.handle.net/11365/21963
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