Convexity of the support of the displacement interpolation: Counterexamples

Filippo Santambrogio*, Xu Jia Wang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    Given two smooth and positive densities ρ0,ρ1 on two compact convex sets K0,K1, respectively, we consider the question whether the support of the measure ρt obtained as the geodesic interpolant of ρ0 and ρ1 in the Wasserstein space W2(Rd) is necessarily convex or not. We prove that this is not the case, even when ρ0 and ρ1 are uniform measures.

    Original languageEnglish
    Pages (from-to)152-158
    Number of pages7
    JournalApplied Mathematics Letters
    Volume58
    DOIs
    Publication statusPublished - 1 Aug 2016

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