Spindle Convexity

  • Horst MartiniEmail author
  • Luis Montejano
  • Déborah Oliveros


Let h be a positive real number and let p and q be two points in Euclidean n-space \(\mathbb {E}^n\), no more than 2h apart. The h-interval determined by this pair of points is the intersection of all balls of radius h that contain p and q. We say that a set \(\phi \), with diameter less than or equal to 2h, is spindle h-convex if given a pair of points p and q in \(\phi \), the h-interval they determine is also in \(\phi \).

Supplementary material

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Horst Martini
    • 1
    Email author
  • Luis Montejano
    • 2
  • Déborah Oliveros
    • 2
  1. 1.Faculty of MathematicsChemnitz University of TechnologyChemnitzGermany
  2. 2.Instituto de MatemáticasUniversidad Nacional Autónoma de México, Campus JuriquillaQuerétaroMéxico

Personalised recommendations