Remarks on Lipschitz geometry on globally conic singular manifolds

Abstract

We study metric properties of manifolds with conic singularities and present a natural interplay between metrically conic and metrically asymptotically conic behaviour. As a consequence, we prove that a singular sub-manifold is Lipschitz normally embedded, i.e. its inner and outer metric structures are equivalent, in an ambient singular manifold, wheneverthe singularities are conic and the ends of the manifold are asymptotically conic, which answers positively a question raised in our last work.