Extending and improving conical bicombings

Abstract

We prove that for every reversible conical bicombing $\sigma$ on a metric space $X$, there exists a conical bicombing on the injective hull of $X$ that extends $\sigma$. We also establish a Descombes-Lang type result stating that every proper metric space with a conical bicombing admits a consistent bicombing satisfying certain convexity conditions.