Shenawy, S. (2019). Horosphere slab separation theorems in manifolds without conjugate points. test, 27(1), 1-6. doi: 10.1186/s42787-019-0038-5
Sameh Shenawy. "Horosphere slab separation theorems in manifolds without conjugate points". test, 27, 1, 2019, 1-6. doi: 10.1186/s42787-019-0038-5
Shenawy, S. (2019). 'Horosphere slab separation theorems in manifolds without conjugate points', test, 27(1), pp. 1-6. doi: 10.1186/s42787-019-0038-5
Shenawy, S. Horosphere slab separation theorems in manifolds without conjugate points. test, 2019; 27(1): 1-6. doi: 10.1186/s42787-019-0038-5

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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