Horosphere slab separation theorems in manifolds without conjugate points | ||
| Journal of the Egyptian Mathematical Society | ||
| Volume 27, Issue 1, 2019, Pages 1-6 PDF (634.91 K) | ||
| DOI: 10.1186/s42787-019-0038-5 | ||
| Author | ||
| Sameh Shenawy | ||
| Department of Mathematics, Modern Academy, Maadi, Cairo, Egypt | ||
| Abstract | ||
| Let Wn 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 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 are considered. | ||
| Keywords | ||
| Horosphere separation; Slab horosphere separation; Manifolds without conjugate points; Separation of convex sets | ||
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