Geometry and volume product of finite dimensional Lipschitz-free spaces

The goal of this paper is to study geometric and extremal properties the convex body BF(M), which unit ball Lipschitz-free Banach space associated with a finite metric M. We investigate ℓ1 ℓ∞-sums, in particular we characterize spaces such that BF(M) Hanner polytope. also whose are isometric. discuss extreme volume product P(M)=|BF(M)|⋅|BF(M)∘|, when number elements M fixed. show if P(M) maximal among all same points, then triangle inequalities strict simplicial. focus on minimizing P(M), Mahler's conjecture for class bodies.