Diameter-extremal subsets of spheres

DOI10.1007/BF02187719zbMath0663.52008MaRDI QIDQ1114164

Mikhail G. Katz

Publication date: 1989

Published in: Discrete \& Computational Geometry (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/131068

zbMATH Keywords

Hausdorff metricspherecritical pointdiameter-extremal set

Mathematics Subject Classification ID

Spherical and hyperbolic convexity (52A55) General theory of distance geometry (51K05)

Related Items (6)

Geometric Approaches to Persistent Homology ⋮ On Vietoris-Rips complexes of hypercube graphs ⋮ The persistent topology of optimal transport based metric thickenings ⋮ Vietoris thickenings and complexes have isomorphic homotopy groups ⋮ The rational filling radius of complex projective space ⋮ Convexity, critical points, and connectivity radius

Cites Work

• The filling radius of two-point homogeneous spaces
• Filling Riemannian manifolds
• The number of faces of a simplicial convex polytope
• Curvature, diameter and Betti numbers
• A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
• A generalized sphere theorem
• The lower bound conjecture for 3- and 4-manifolds
• The numbers of faces of simplicial polytopes
• Über eine Übertragung des Hellyschen Satzes in Sphärische Räume
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