Hyperbolic spaces are of strictly negative type |
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| Authors: | P G Hjorth S L Kokkendorff S Markvorsen |
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| Institution: | Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Lyngby, Denmark ; Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Lyngby, Denmark ; Department of Mathematics, Technical University of Denmark, Building 303, DK-2800 Lyngby, Denmark |
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| Abstract: | 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. |
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| Keywords: | Metric spaces negative type strictly negative type length spaces fundamental group |
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