REMARKS ON LIPSCHITZ GEOMETRY OF GLOBALLY CONIC SINGULAR MANIFOLDS

We study metric properties of manifolds with conic singularities and present a natural interplay between metrically conic and metrically asymptotically conic behavior. 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 whenever the singularities are conic and the ends of the manifold are asymptotically conic, which answers positively a question of Costa et al. (2024c).