S. Reisner

activity

19922018

most citedLocal minimality of the volume-product at the simplex

18 citations · 33 across the 9 of their papers we have counts for

collaborators

10 papers

math.MG2018★ 3 cited

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…

math.MG2015

The isotropy constant and boundary properties of convex bodies

Mathieu Meyer, Shlomo Reisner

Let $K^{n}$ be the set of all convex bodies in $R^{n}$ endowed with the Hausdorff distance. We prove that if $K \in K^{n}$ has positive generalized Gauss curvature a…

math.MG2015★ 5 cited

Volume product of planar polar convex bodies --- lower estimates with stability

K. J. Böröczky, E. Makai, M. Meyer +1

Let $K \subset R^{2}$ be an $o$ -symmetric convex body, and $K^{*}$ its polar body. Then we have $∣ K ∣ \cdot ∣ K^{*} ∣ \geq 8$ , with equality if and only if $K$ is a parallelogram. (…

math.FA2010★ 4 cited

A note on Mahler's conjecture

Shlomo Reisner, Carsten Schütt, Elisabeth M. Werner

Let $K$ be a convex body in $R^{n}$ with Santaló point at 0\. We show that if $K$ has a point on the boundary with positive generalized Gauß curvature, then the volume produ…

math.FA2010

The GL-l.u.st.\ constant and asymmetry of the Kalton-Peck twisted sum in finite dimensions

Y. Gordon, M. Junge, M. Meyer +1

We prove that the Kalton-Peck twisted sum $Z_{2}^{n}$ of $n$ -dimensional Hilbert spaces has GL-l.u.st.\ constant of order $lo g n$ and bounded GL constant. This is the first concrete e…

math.MG2010★ 18 cited

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…