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Award ID contains: 2005279

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  1. We show that metric trees and their products meet the octahedron comparison, which is a certain six-point metric comparison similar to Alexandrov’s CAT(0) comparison. 
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    Free, publicly-accessible full text available October 1, 2026
  2. A metric space is said to be all-set-homogeneous if any isometry between its subsets can be extended to an isometry of the whole space. A classification of a certain subclass of all-set-homogeneous length spaces is given. 
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  3. We give an if-and-only-if condition on five-point metric spaces that admit isometric embeddings into complete nonnegatively curved Riemannian manifolds. 
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