Department of Mathematics, Modern Academy, Maadi, Cairo, Egypt
https://doi.org/10.1186/s42787-019-0038-5
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.
Shenawy, S. (2019). Horosphere slab separation theorems in manifolds without conjugate points. Journal of the Egyptian Mathematical Society, 27(1), 1-6. doi: https://doi.org/10.1186/s42787-019-0038-5
MLA
Sameh Shenawy. "Horosphere slab separation theorems in manifolds without conjugate points", Journal of the Egyptian Mathematical Society, 27, 1, 2019, 1-6. doi: https://doi.org/10.1186/s42787-019-0038-5
HARVARD
Shenawy, S. (2019). 'Horosphere slab separation theorems in manifolds without conjugate points', Journal of the Egyptian Mathematical Society, 27(1), pp. 1-6. doi: https://doi.org/10.1186/s42787-019-0038-5
VANCOUVER
Shenawy, S. Horosphere slab separation theorems in manifolds without conjugate points. Journal of the Egyptian Mathematical Society, 2019; 27(1): 1-6. doi: https://doi.org/10.1186/s42787-019-0038-5
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