Generalizations of Casey’s Theorem for Higher Dimensions
- Авторы: Abrosimov N.1,2, Aseev V.1
-
Учреждения:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Выпуск: Том 39, № 1 (2018)
- Страницы: 1-12
- Раздел: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/200758
- DOI: https://doi.org/10.1134/S199508021801002X
- ID: 200758
Цитировать
Аннотация
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.
Ключевые слова
Об авторах
N. Abrosimov
Sobolev Institute of Mathematics; Novosibirsk State University
Автор, ответственный за переписку.
Email: abrosimov@math.nsc.ru
Россия, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 2, Novosibirsk, 630090
V. Aseev
Sobolev Institute of Mathematics
Email: abrosimov@math.nsc.ru
Россия, pr. Akad. Koptyuga 4, Novosibirsk, 630090