Explicit Geodesics in Gromov-Hausdorff Space

2016/03/08 by Chowdhury, Samir, Mémoli, Facundo · 1 citation
#FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1603.02385

Abstract

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 \mathbbS⁰ and \mathbbSⁿ for any n≥ 1.

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