Generalizations of Casey’s Theorem for Higher Dimensions

N. V. Abrosimov, V. V. Aseev

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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
Volume39
Issue number1
DOIs
Publication statusPublished - 1 Jan 2018

Keywords

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

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