An Improved Volume Ratio Bound via Isotropic Positions

Daniel Galicer, Mariano Merzbacher, Damián Pinasco +1

We show that, for every pair of convex bodies $K,L\subset {\mathbb{R}}^n$, $$\mathrm{vr}(K,L)\le C\sqrt{n\log (n+1)}.$$ The main point is to place $K$ and $L^{\circ }$ in isotropi…