Generalizations of Casey’s Theorem for Higher Dimensions

Generalizations of Casey’s Theorem for Higher Dimensions Full article

Journal

Lobachevskii Journal of Mathematics
ISSN: 1995-0802 , E-ISSN: 1818-9962

Output data

Year: 2018, Volume: 39, Number: 1, Pages: 1-12 Pages count : 12 DOI: 10.1134/S199508021801002X

Tags

Casey’s theorem; problem of Apollonius; Ptolemy’s theorem

Authors

Abrosimov N.V. ^1,2 , Aseev V.V. ¹

Affiliations

1	Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russian Federation
2	Novosibirsk State University, ul. Pirogova 2, Novosibirsk, 630090, Russian Federation

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. © 2018, Pleiades Publishing, Ltd.

Abrosimov N.V. , Aseev V.V.
Generalizations of Casey’s Theorem for Higher Dimensions
Lobachevskii Journal of Mathematics. 2018. V.39. N1. P.1-12. DOI: 10.1134/S199508021801002X WOS Scopus OpenAlex

Web of science:	WOS:000424907400001
Scopus:	2-s2.0-85042129212
OpenAlex:	W2792251774

DB	Citing
Scopus	5
OpenAlex	7
Web of science	4