Email this article Generalizations of Casey’s Theorem for Higher Dimensions
- Authors: Abrosimov N.V.1,2, Aseev V.V.1
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 39, No 1 (2018)
- Pages: 1-12
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200758
- DOI: https://doi.org/10.1134/S199508021801002X
- ID: 200758
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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.
About the authors
N. V. Abrosimov
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: abrosimov@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
V. V. Aseev
Sobolev Institute of Mathematics
Email: abrosimov@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090
