A non-compact convex hull in generalized non-positive curvature
Basso, G., Krifka, Y., & Soultanis, E. (2024). A non-compact convex hull in generalized non-positive curvature. Mathematische Annalen, Early online. https://doi.org/10.1007/s00208-024-02905-w
Julkaistu sarjassa
Mathematische AnnalenPäivämäärä
2024Tekijänoikeudet
© 2024 the Authors
Gromov’s (open) question whether the closed convex hull of finitely many points in a complete CAT(0) space is compact naturally extends to weaker notions of non-positive curvature in metric spaces. In this article, we consider metric spaces admitting a conical geodesic bicombing, and show that the question has a negative answer in this setting. Specifically, for each n > 1, we construct a complete metric space X admitting a conical geodesic bicombing, which is the closed convex hull of n points and is not compact. The space X moreover has the universal property that for any n points A = {x1,..., xn} ⊂ Y in a complete CAT(0) space Y there exists a Lipschitz map f : X → Y such that the convex hull of A is contained in f (X).
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0025-5831Asiasanat
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https://converis.jyu.fi/converis/portal/detail/Publication/216071950
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