Horosphere slab separation theorems in manifolds without conjugate points
Abstract Let Wn $\mathcal {W}^{n}$ be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let W∈Wn $W\in \mathcal {W}^{n}$ and let A and B be two convex subsets of W. This note aim...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-09-01
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| Series: | Journal of the Egyptian Mathematical Society |
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| Online Access: | http://link.springer.com/article/10.1186/s42787-019-0038-5 |
| Summary: | Abstract Let Wn $\mathcal {W}^{n}$ be the set of smooth complete simply connected n-dimensional manifolds without conjugate points. The Euclidean space and the hyperbolic space are examples of these manifolds. Let W∈Wn $W\in \mathcal {W}^{n}$ and let A and B be two convex subsets of W. This note aims to investigate separation and slab horosphere separation of A and B. For example,sufficient conditions on A and B to be separated by a slab of horospheres are obtained. Existence and uniqueness of foot points and farthest points of a convex set A in W∈W $W\in \mathcal {W}$ are considered. |
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| ISSN: | 2090-9128 |