GROMOV--HAUSDORFF DISTANCES BETWEEN NORMED SPACES
Matematički VesnikIn the present paper we study the original Gromov-Hausdorff distance between real normed spaces. In the first part of the paper we prove that two finite-dimensional real normed spaces on a finite Gromov-Hausdorff distance are isometric to each other.
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Unified topological inference for brain networks in temporal lobe epilepsy using the Wasserstein distance. [PDF]
Neuroimage, 2023 Chung MK +9 more
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Surface measure on, and the local geometry of, sub-Riemannian manifolds. [PDF]
Calc Var Partial Differ Equ, 2023 Don S, Magnani V.
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Moduli spaces of compact RCD(0,N)-structures. [PDF]
Math Ann, 2023 Mondino A, Navarro D.
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Fundamentals of Theory of Continuous Gromov--Hausdorff distance
The Gromov--Hausdorff distance (hereinafter referred to as the GH-distance) is a measure of non-isometricity of metric spaces. In this paper, we study a modification of this distance that also takes topological differences into account. The resulting function of pairs of metric spaces is called the continuous GH-distance.
Bogaty, Semeon A., Tuzhilin, Alexey A.
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On the existence of isoperimetric regions in manifolds with nonnegative Ricci curvature and Euclidean volume growth. [PDF]
Calc Var Partial Differ Equ, 2022 Antonelli G +3 more
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The G-Gromov-Hausdorff Distance and Equivariant Topology
For each arbitrary finite group $G$, we consider a suitable notion of Gromov Hausdorff distance between compact $G$ metric spaces and derive lower bounds based on equivariant topology methods. As applications, we prove equivariant rigidity and finiteness theorems, and obtain sharp bounds on the Gromov Hausdorff distance between spheres.
Lim, Sunhyuk, Memoli, Facundo
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An Introduction to Topological Data Analysis: Fundamental and Practical Aspects for Data Scientists. [PDF]
Front Artif Intell, 2021 Chazal F, Michel B.
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On the Gromov-Hausdorff distance between compact spaces
, 2023 This work provides an introduction to the Gromov-Hausdorff distance, discussing its original definition and its relationship with correspondences between spaces. We prove that the Gromov-Hausdorff distance serves as a metric for the set of isometry classes of compact metric spaces.
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Lipschitz Carnot-Carathéodory Structures and their Limits. [PDF]
J Dyn Control Syst, 2023 Antonelli G +2 more
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