Topic
Hyperbolic coordinates
About: Hyperbolic coordinates is a research topic. Over the lifetime, 656 publications have been published within this topic receiving 10010 citations.
Papers published on a yearly basis
1 / 2
Papers
TL;DR: In this paper, the authors introduce a new technique for finding CAT(1) surfaces in hyperbolic 3-manifolds, and they use this technique to show that a complete 3-Manifold with finitely generated fundamental group is geometrically and topologically tame.
Abstract: We introduce a new technique for finding CAT(-1) surfaces in hyperbolic 3-manifolds. We use this to show that a complete hyperbolic 3-manifold with finitely generated fundamental group is geometrically and topologically tame.
334 citations
TL;DR: In this article, it was shown that any nontrivial solution of certain nonlinear hyperbolic partial differential equations of second order blows up in a finite time if the initial data are localized, the initial velocity being on the average non-negative.
Abstract: We prove that any nontrivial solution of certain nonlinear hyperbolic partial differential equations of second order blows up in a finite time if the initial data are localized, the initial velocity being on the average non-negative.
241 citations
TL;DR: The Hyperbolic Number Plane (HPN) as discussed by the authors is a hyperbolic number plane that is a special case of the number plane of the HPN, and it can be represented as follows
Abstract: (1995). The Hyperbolic Number Plane. The College Mathematics Journal: Vol. 26, No. 4, pp. 268-280.
222 citations
TL;DR: The necessary and sufficient conditions for shell crossings and regular maxima in the Tolman model were derived in this article, and it was shown that the properties that distinguish shell crossings from more serious singularities in spherical symmetry are independent of the equation of state.
Abstract: We consider the problem of shell crossings and regular maxima in the Tolman model. The necessary and sufficient conditions which guarantee no shell crossings will arise in Tolman models are derived, and we show explicitly that a Tolman model (in general, with a surface layer) may contain both elliptic and hyperbolic regions without developing any shell crossings and without the hyperbolic regions recollapsing. This finding is contrary to the recent hypothesis of Zel'dovich and Grishchuk. We also show that the properties that distinguish shell crossings from more serious singularities in spherical symmetry are independent of the equation of state.
189 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2025 | 2 |
| 2024 | 2 |
| 2023 | 3 |
| 2022 | 7 |
| 2021 | 3 |
| 2020 | 7 |