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Register a new userOn geodesic extendibility and the space of compact balls of length spaces
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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 $(Sigma (X),d_H)$ of compact balls endowed with the Hausdorff distance and give an explicit isometry between $(Sigma (X),d_H)$ and the closed half-space $ Xtimes mathbb{R}_{ge 0}$ endowed with a taxicab metric. Among the applications we establish a group isometry between $mbox{Iso} (X,d)$ and $mbox{Iso} (Sigma (X),d_H)$ when $(X,d)$ is a Hadamard space.
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