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2016

Explicit Geodesics in Gromov-Hausdorff Space

Chowdhury, Samir, Mémoli, Facundo

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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 $n\geq 1$.

Explicit Geodesics in Gromov-Hausdorff Space · Around

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Misha Gromov, Metric structures for Riemannian and non-Riemannian spaces , Progress in Mathematics, vol. 152, Birkhäuser Boston Inc., Boston, MA, 1999
1999
Earlier work this paper cites.
Dmitri Burago, Yuri Burago, and Sergei Ivanov, A course in metric geometry , AMS Graduate Studies in Math., vol. 33, American Mathematical Society, 2001
2001
Earlier work this paper cites.
Allen Hatcher, Algebraic topology , Cambridge University Press, 2002
2002
Earlier work this paper cites.

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