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The Gromov-Hausdorff Metric on the Space of Compact Metric Spaces is Strictly Intrinsic

· 2015 · math.MG · arXiv 1504.03830

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abstract

It is proved that the Gromov-Hausdorff metric on the space of compact metric spaces considered up to an isometry is strictly intrinsic, i.e., the corresponding metric space is geodesic. In other words, each two points of this space (each two compact metric spaces) can be connected by a geodesic. For finite metric spaces a geodesic is constructed explicitly.

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math.MG 1

years

2019 1

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UNVERDICTED 1

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Gromov--Hausdorff Distance to Simplexes

math.MG · 2019-06-23 · unverdicted · novelty 5.0

Extends prior Gromov-Hausdorff distance results to simplexes from compact metric spaces to all bounded ones via partition geometry.

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  • Gromov--Hausdorff Distance to Simplexes math.MG · 2019-06-23 · unverdicted · none · ref 8 · internal anchor

    Extends prior Gromov-Hausdorff distance results to simplexes from compact metric spaces to all bounded ones via partition geometry.