18 citations · 33 across the 9 of their papers we have counts for
6 papers · 1 filter
Ellipsoids are the only local maximizers of the volume product
Mathieu Meyer, Shlomo Reisner
Using previous results about shadow systems and Steiner symmetrization, we prove that the local maximizers of the volume product of convex bodies are actually the global maximizers…
The isotropy constant and boundary properties of convex bodies
Mathieu Meyer, Shlomo Reisner
Let be the set of all convex bodies in endowed with the Hausdorff distance. We prove that if has positive generalized Gauss curvature a…
Volume product of planar polar convex bodies --- lower estimates with stability
K. J. Böröczky, E. Makai, M. Meyer +1
Let be an -symmetric convex body, and its polar body. Then we have , with equality if and only if is a parallelogram. (…
Local minimality of the volume-product at the simplex
Jaegil Kim, Shlomo Reisner
It is proved that the simplex is a strict local minimum for the volume product, P(K)=min(vol(K) vol(K^z)), K^z is the polar body of K with respect to z, the minimum is taken over z…
Shadow systems and volume of polar convex bodies
Mathieu Meyer, Shlomo Reisner
We prove that the reciprocal of the volume of the polar bodies, about the Santaló point, of a {\em shadow system} of convex bodies , is a convex function of . Thus extendin…
Umbrellas and polytopal approximation of the euclidean ball
Yehoram Gordon, Shlomo Reisner, Carsten Schütt
There are two positive, absolute constants and so that the volume of the difference set of the -dimensional Euclidean ball and an inscribed polytope with n verti…