The Cartan–Hadamard Theorem for metric spaces with local geodesic bicombings
Benjamin MieschETH Zürich, Switzerland
We prove the Cartan–Hadamard Theorem for spaces which are not necessarily uniquely geodesic but locally possess a suitable selection of geodesics, a so-called convex geodesic bicombing.
Furthermore, we deduce a local-to-global theorem for injective (or hyperconvex) metric spaces, saying that under certain conditions a complete, simply-connected, locally injective metric space is injective. A related result for absolute 1-Lipschitz retracts follows.
Cite this article
Benjamin Miesch, The Cartan–Hadamard Theorem for metric spaces with local geodesic bicombings. Enseign. Math. 63 (2017), no. 1/2, pp. 233–247DOI 10.4171/LEM/63-1/2-8