Classical and continuous Gromov-Hausdorff distances
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Semenov, K. V., Tuzhilin, A. A.
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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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Lower Bounding the Gromov--Hausdorff distance in Metric Graphs
Let $G$ be a finite, connected metric graph and let $X\subseteq G$ be a subset. If $X$ is sufficiently dense in $G$, we show that the Gromov--Hausdorff distance matches the Hausdorff distance, namely $d_\gh(G,X)=d_\h(G,X)$. When the metric graph is the circle $G=S^1$ with circumference $2π$, a recent study established the equality $d_\gh(S^1,X)=d_\h(S ...
Adams, Henry +4 more
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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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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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Lectures on Hausdorff and Gromov-Hausdorff Distance Geometry
, 2020 The course was given at Peking University, Fall 2019. We discuss the following subjects: (1) Introduction to general topology, hyperspaces, metric and pseudometric spaces, graph theory. (2) Graphs in metric spaces, minimum spanning tree, Steiner minimal tree, Gromov minimal filling.
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Moduli spaces of compact RCD(0,N)-structures. [PDF]
Math Ann, 2023 Mondino A, Navarro D.
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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 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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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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