Generalizations of Casey’s Theorem for Higher Dimensions

N. V. Abrosimov, V. V. Aseev

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1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalLobachevskii Journal of Mathematics
Issue number1
Publication statusPublished - 1 Jan 2018


  • Casey’s theorem
  • problem of Apollonius
  • Ptolemy’s theorem
  • Casey's theorem
  • Ptolemy's theorem


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