Hyperbolic spaces are of strictly negative type

Poul G. Hjorth, Simon L. Kokkendorff, Steen Markvorsen

    Research output: Contribution to journalJournal articleResearchpeer-review


    We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.
    Original languageEnglish
    JournalProceedings of the American Mathematical Society
    Issue number1
    Pages (from-to)175-181
    Publication statusPublished - 2002

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