Corpus ID: 237491048

Compact sets and the closure of their convex hulls in CAT(0) spaces

  title={Compact sets and the closure of their convex hulls in CAT(0) spaces},
  author={Arian Berdellima},
We study the closure of the convex hull of a compact set in a complete CAT(0) space. First we give characterization results in terms of compact sets and the closure of their convex hulls for locally compact CAT(0) spaces that are either regular or satisfy the geodesic extension property. Later inspired by a geometric interpretation of Carathéodory’s Theorem we introduce the operation of threading for a given set. We show that threading exhibits certain monotonicity properties with respect to… Expand

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