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arXiv · 2105.04377

On geodesic extendibility and the space of compact balls of length spaces

Waldemar Barrera·Luis M. Montes De Oca·Didier A. Solis
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Abstract

In this work we study the issue of geodesic extendibility on complete and locally compact metric length spaces. We focus on the geometric structure of the space $(Σ(X),d_H)$ of compact balls endowed with the Hausdorff distance and give an explicit isometry between $(Σ(X),d_H)$ and the closed half-space $ X\times \mathbb{R}_{\ge 0}$ endowed with a taxicab metric. Among the applications we establish a group isometry between $\mbox{Iso} (X,d)$ and $\mbox{Iso} (Σ(X),d_H)$ when $(X,d)$ is a Hadamard space.

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Waldemar Barrera, Luis M. Montes De Oca, Didier A. Solis. 2021-05-27. On geodesic extendibility and the space of compact balls of length spaces. https://doi.org/10.1007/s00605-021-01566-0

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