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- W3098597630 abstract "The goal of this paper is to study geometric and extremal properties of the convex body BF(M), which is the unit ball of the Lipschitz-free Banach space associated with a finite metric space M. We investigate ℓ1 and ℓ∞-sums, in particular we characterize the metric spaces such that BF(M) is a Hanner polytope. We also characterize the finite metric spaces whose Lipschitz-free spaces are isometric. We discuss the extreme properties of the volume product P(M)=|BF(M)|⋅|BF(M)∘|, when the number of elements of M is fixed. We show that if P(M) is maximal among all the metric spaces with the same number of points, then all triangle inequalities in M are strict and BF(M) is simplicial. We also focus on the metric spaces minimizing P(M), and on Mahler's conjecture for this class of convex bodies." @default.
- W3098597630 created "2020-11-23" @default.
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- W3098597630 date "2021-02-01" @default.
- W3098597630 modified "2023-09-30" @default.
- W3098597630 title "Geometry and volume product of finite dimensional Lipschitz-free spaces" @default.
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- W3098597630 doi "https://doi.org/10.1016/j.jfa.2020.108849" @default.
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