Geodesic bicombings on some hyperspaces

@article{Fox2022GeodesicBO,
  title={Geodesic bicombings on some hyperspaces},
  author={Logan S. Fox},
  journal={Journal of Geometry},
  year={2022}
}
  • L. Fox
  • Published 23 June 2021
  • Mathematics
  • Journal of Geometry
We show that if (X, d) is a metric space which admits a consistent convex geodesic bicombing, then we can construct a conical bicombing on CB(X), the hyperspace of nonempty, closed, bounded, and convex subsets of X (with the Hausdorff metric). If X is a normed space or an R-tree, this same method produces a consistent convex bicombing on CB(X). We follow this by examining a geodesic bicombing on the nonempty compact subsets of X , assuming X is a proper metric space. 
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