# American Institute of Mathematical Sciences

2018, 25: 48-59. doi: 10.3934/era.2018.25.006

## Explicit geodesics in Gromov-Hausdorff space

 Department of Mathematics, The Ohio State University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210. Phone: (614) 292-4975, Fax: (614) 292-1479

Received  March 31, 2017 Revised  March 13, 2018 Published  June 2018

Fund Project: This work was supported by NSF grants CCF-1526513 and IIS-1422400.

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 $n\geq 1$.

Citation: Samir Chowdhury, Facundo Mémoli. Explicit geodesics in Gromov-Hausdorff space. Electronic Research Announcements, 2018, 25: 48-59. doi: 10.3934/era.2018.25.006
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