Gromov-Hausdorff distances between quotient metric spaces
The Hausdorff distance measures how far apart two sets are in a common metric space. By contrast, the Gromov-Hausdorff distance provides a notion of distance between two abstract metric spaces. How do these distances behave for quotients of spaces under group actions? Suppose a group $G$ acts by isometries on two metric spaces $X$ and $Y$.
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The G-Gromov-Hausdorff Distance and Equivariant Topology
We made the following changes: (1) reorganized the section order, (2) added a subsection on the Gromov-Hausdorff distance between quotient spaces, and (3) added more examples and remarks.
Lim, Sunhyuk, Memoli, Facundo
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Probab Theory Relat Fields, 2022 Aoun R, Sert C.
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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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Acta Math Sin Engl Ser, 2022 Liu J, Xia KL, Wu J, Yau SS, Wei GW.
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