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Explicit geodesics in Gromov-Hausdorff space

This work was supported by NSF grants CCF-1526513 and IIS-1422400

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  • We provide an alternative, constructive proof that the collection ${\mathcal{M}}$ of isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance is a geodesic space. The core of our proof is a construction of explicit geodesics on ${\mathcal{M}}$. We also provide several interesting examples of geodesics on ${\mathcal{M}}$, including a geodesic between ${\mathbb{S}}^0$ and ${\mathbb{S}}^n$ for any $n\geq 1$.

    Mathematics Subject Classification: Primary 53C23, Secondary 51F99.


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  • Figure 1.  Branching geodesics as described in §1.1.2

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