Lobachevskii Journal of Mathematics

, Volume 39, Issue 1, pp 1–12 | Cite as

Generalizations of Casey’s Theorem for Higher Dimensions

  • N. V. AbrosimovEmail author
  • V. V. Aseev


We give generalizations of Casey’s theorem and its converse for higher dimensions. We also present a multidimensional generalization for the problem of Apollonius. To do this we introduce a notion of ψ-tangent for a generalized k-sphere that touches a number of generalized n-balls in proper manner.

Keywords and phrases

Casey’s theorem Ptolemy’s theorem problem of Apollonius 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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