On volume product inequalities for convex sets

By S. Campi, Paolo Gronchi. 2006

76 citations recorded by the source corpus.

The volume of the polar body of a symmetric convex set K of R d is investigated. It is shown that its reciprocal is a convex function of the time t along movements, in which every point of K moves with constant speed parallel to a fixed direction. This result is applied to find reverse forms of the L p -Blaschke-Santalo inequality for two-dimensional convex sets.

Subfields: Applied Mathematics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/d61db615d5fc2b8cc621a8c5afd1c66849dbaea4

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In Applied Mathematics

In Molecular Biology

Citations in the corpus

Shadow Systems and Volumes of Polar Convex Bodies (2006, result): “| is a convex function of t. The concept was further investigated by Shephard [21] who, among other results, extended the convexity result to mixed volumes. Campi and Gronchi proved in a recent paper [6]: If Kt is a shadow system of origin symmetric convex bodies in Rd, then |K∗ t| −1 is a convex fu”
The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”
Shadow systems of asymmetric Lp zonotopes (2013, background): “2 was discovered recently: Campi and Gronchi, in the case of origin-symmetric convex bodies, have established that the volume of polars of shadow systems of convex bodies with respect to the Santaló point is the inverse of a convex function [6].”
A new proof of the Orlicz Busemann-Petty centroid inequality (2011, methodology): “So our work is a natural extension of the work of Campi and Gronchi [2].”