Diameter-extremal subsets of spheres

Abstract

We investigate those spherical point sets which, relative to the Hausdorff metric, give local minima of the diameter function, and obtain estimates which, in principle, justify computer-generated configurations. We test the new sets against two classical conjectures: Borsuk's and McMullen's.

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Supported in part by NSF Grant DMS 8602645.

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Katz, M. Diameter-extremal subsets of spheres. Discrete Comput Geom 4, 117–137 (1989). https://doi.org/10.1007/BF02187719

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Keywords

  • Discrete Comput Geom
  • North Pole
  • Minimal Subset
  • Contracting Coefficient
  • Diameter Restriction