5 papers
An Improved Volume Ratio Bound via Isotropic Positions
Daniel Galicer, Mariano Merzbacher, Damián Pinasco
We show that, for every pair of convex bodies , The main point is to place and in isotropi…
On the volume ratio of projections of convex bodies
Daniel Galicer, Alexander E. Litvak, Mariano Merzbacher +1
We study the volume ratio between projections of two convex bodies. Given a high-dimensional convex body we show that there is another convex body such that the volume rati…
Continuous quantitative Helly-type results
Tomás Fernandez Vidal, Daniel Galicer, Mariano Merzbacher
Brazitikos' results on quantititative Helly-type theorems (for the volume and for the diameter) rely on the work of Srivastava on sparsification of John's decompositions. We change…
Asymptotic estimates for the largest volume ratio of a convex body
Daniel Galicer, Mariano Merzbacher, Damián Pinasco
The largest volume ratio of given convex body is defined as $$\mbox{lvr}(K):= \sup_{L \subset \mathbb{R}^n} \mbox{vr}(K,L),$$ where the runs over al…
The minimal volume of simplices containing a convex body
Daniel Galicer, Mariano Merzbacher, Damián Pinasco
Let be a convex body with barycenter at the origin. We show there is a simplex having also barycenter at the origin such that $\left(\frac{vol…