Horosphere slab separation theorems in manifolds without conjugate points - Egyptian Knowledge Bank

383506

Horosphere slab separation theorems in manifolds without conjugate points

Article

Last updated: 31 Dec 2024

Subjects

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.

DOI

10.1186/s42787-019-0038-5

Keywords

Horosphere separation, Slab horosphere separation, Manifolds without conjugate points, Separation of convex sets

Authors

View Authors

First Name

Sameh

Last Name

Shenawy

MiddleName

Affiliation

Department of Mathematics, Modern Academy, Maadi, Cairo, Egypt

Email

City

Orcid

Volume

Article Issue

Related Issue

50652

Issue Date

2019-12-01

Receive Date

2024-10-02

Publish Date

2019-12-01

Page Start

Page End

Print ISSN

1110-256X

Online ISSN

2090-9128

Article File

JOEMS_Volume 27_Issue 1_Pages 1-6.pdf

PDF . 650.1kB

Link

https://joems.journals.ekb.eg/article_383506.html

Detail API

https://joems.journals.ekb.eg/service?article_code=383506

Order

383,506

Publication Type

Journal

Publication Title

Journal of the Egyptian Mathematical Society

Publication Link

https://joems.journals.ekb.eg/

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