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Hausdorff Implementation of Linear Geodesics in the Gromov–Hausdorff Space
An implementation of a “rectilinear” geodesic lying in the Gromov–Hausdorff space is constructed in the form of the shortest geodesic with respect to...
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Particular Cases of Quasi-Parallelograms of Type I on the Lobachevsky Plane
In this paper, we consider particular cases of quasi-parallelograms, which are obtained by transferring to the Lobachevsky plane various...
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Nonexistence of the Quasi-harmonic Spheres and Harmonic Spheres into Certain Manifold
We mainly study the nonexistence of quasi-harmonic spheres and harmonic spheres into spheres of any dimension which omits a neighbourhood of totally...
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Special Cases of Hyperbolic Parallelograms on the Lobachevsky Plane
In this paper, we consider particular cases of hyperbolic parallelograms obtained by transferring characteristic properties of rectangles and squares...
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The Planck boundary within the hyperspace of the circle of pseudo-arcs
In this paper we point out an interesting geometric structure of nonnegative metric curvature emerging from the hyperspaces of decomposable,...
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Dual Linear Programming Problem and One-Dimensional Gromov Minimal Fillings of Finite Metric Spaces
The present paper is devoted to the study of minimal parametric fillings of finite metric spaces (a version of optimal connection problem) by linear...
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Quasi-convex subsets in Alexandrov spaces with lower curvature bound
We introduce quasi-convex subsets in Alexandrov spaces with lower curvature bound, which include not only all closed convex subsets without boundary...
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Persistence Approximation Property for Maximal Roe Algebras
Persistence approximation property was introduced by Hervé Oyono-Oyono and Guoliang Yu. This property provides a geometric obstruction to Baum-Connes...
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A new inductive approach for counting dimension in large scale
We introduce the notion of large scale dimensiongrad as a large scale invariant of asymptotic resemblance spaces. Consequently it can be considered...
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Straight projective-metric spaces with centres
It is proved that a straight projective-metric space has an open set of centres, if and only if it is either the hyperbolic or a Minkowskian...
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A Sufficient Condition to a Regular Set Being of Positive Measure on Spaces
In this paper, we study regular sets in metric measure spaces with Ricci curvature bounded from below. We prove that the existence of a point in the...
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Conformal Transformation on Metric Measure Spaces
We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and...
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A perimeter-based angle measure in Minkowski planes
Measuring angles in the Euclidean plane is a well-known topic, but for general normed planes there exists a variety of different concepts. These can...
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Extension Theorems for Large Scale Spaces via Coarse Neighbourhoods
We introduce the notion of (hybrid) large scale normal space and prove coarse geometric analogues of Urysohn’s Lemma and the Tietze Extension Theorem...
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Fermat–Steiner problem in the metric space of compact sets endowed with Hausdorff distance
Fermat–Steiner problem consists in finding all points in a metric space Y such that the sum of distances from each of them to the points from some...
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Circle Numbers of Regular Convex Polygons
The circle number function is extended here to regular convex polygons. To this end, the radius of the polygonal circle is defined as the Minkowski...
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Coarse embedding into uniformly convex Banach spaces
In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding...
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On the geometry of flat surfaces with a single singularity
If T is a flat torus with boundary and a conical singularity in its boundary then the isometry type of T is determined by the lengths of five closed...
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Magnitude, Diversity, Capacities, and Dimensions of Metric Spaces
Magnitude is a numerical invariant of metric spaces introduced by Leinster, motivated by considerations from category theory. This paper extends the...
