On a conjecture of Candelas and de la Ossa

Abstract: We prove that the metric completion of a canonical Ricci-flat Kahler metric on the nonsingular part of a projective Calabi-Yau variety $X$ with ordinary double point singularities, is a compact metric length space homeomorphic to the projective variety $X$ itself. As an application, we prove a conjecture of Candelas and de la Ossa for conifold flops and transitions.