scholarly journals Mutually nearest and farthest points of sets and the Drop Theorem in geodesic spaces

2010 ◽  
Vol 165 (2) ◽  
pp. 173-197 ◽  
Author(s):  
Rafa Espínola ◽  
Adriana Nicolae
Keyword(s):  
Farthest Points ◽  
Geodesic Spaces ◽  
Drop Theorem

Some results on farthest points

2016 ◽  
Vol 46 (1) ◽  
pp. 207-215
Author(s):  
F. Soleimany ◽  
M. Iranmanesh
Keyword(s):  
Farthest Points

scholarly journals Horosphere slab separation theorems in manifolds without conjugate points

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Sameh Shenawy
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Existence And Uniqueness ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Conjugate Points ◽  
Separation Theorems ◽  
Farthest Points ◽  
Simply Connected ◽  
Convex Subsets

Abstract Let $\mathcal {W}^{n}$ 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 $W\in \mathcal {W}^{n}$ W ∈ 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 $W\in \mathcal {W}$ W ∈ W are considered.

scholarly journals Some Continuation results in Uniquely Geodesic Spaces

2021 ◽  
Vol 1850 (1) ◽  
pp. 012046
Author(s):  
V.V. Sreya ◽  
P. Shaini
Keyword(s):  
Geodesic Spaces

scholarly journals Farthest points on most Alexandrov surfaces

2020 ◽  
Vol 20 (1) ◽  
pp. 139-148
Author(s):  
Joël Rouyer ◽  
Costin Vîlcu
Keyword(s):  
Distance Functions ◽  
Farthest Points ◽  
Baire Categories ◽  
Bounded Below

AbstractWe study global maxima of distance functions on most Alexandrov surfaces with curvature bounded below, where most is used in the sense of Baire categories.

scholarly journals On Simultaneous Farthest Points in

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Sh. Al-Sharif ◽  
M. Rawashdeh
Keyword(s):  
Banach Space ◽  
Bounded Subset ◽  
Farthest Points ◽  
Integrable Functions

Let be a Banach space and let be a closed bounded subset of . For , we set  . The set is called simultaneously remotal if, for any , there exists such that  . In this paper, we show that if is separable simultaneously remotal in , then the set of -Bochner integrable functions, , is simultaneously remotal in . Some other results are presented.

scholarly journals Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth have Finitely Generated Fundamental Groups

2015 ◽  
Vol 58 (4) ◽  
pp. 787-798 ◽  
Author(s):  
Yu Kitabeppu ◽  
Sajjad Lakzian
Keyword(s):  
Diameter Growth ◽  
Fundamental Groups ◽  
Finitely Generated ◽  
Finite Generation ◽  
Alexandrov Spaces ◽  
Geodesic Spaces ◽  
Special Case ◽  
Linear Diameter

AbstractIn this paper, we generalize the finite generation result of Sormani to non-branching RCD(0, N) geodesic spaces (and in particular, Alexandrov spaces) with full supportmeasures. This is a special case of the Milnor’s Conjecture for complete non-compact RCD(0, N) spaces. One of the key tools we use is the Abresch–Gromoll type excess estimates for non-smooth spaces obtained by Gigli–Mosconi.

scholarly journals Convexity preserving properties for Hamilton-Jacobi equations in geodesic spaces

2019 ◽  
Vol 39 (1) ◽  
pp. 157-183
Author(s):  
Qing Liu ◽  
◽  
Atsushi Nakayasu ◽  
Keyword(s):  
Geodesic Spaces ◽  
Jacobi Equations
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