Explicit geodesics in Gromov-Hausdorff space

Samir Chowdhury, Facundo Mémoli
2018 Electronic Research Announcements in Mathematical Sciences  
We provide an alternative, constructive proof that the collection 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 M. We also provide several interesting examples of geodesics on M, including a geodesic between S 0 and S n for any n ≥ 1.
doi:10.3934/era.2018.25.006 fatcat:w2mu24gt7bgjxfm623efjclt64