Alexandrov Space

An Alexandrov space with curvature bounded below by is a complete finite-dimensional geodesic metric space whose geodesic triangles satisfy lower comparison with the simply connected surface of constant curvature . Distances between corresponding points on triangle sides are at least the model distances, at the permitted model scale when . This lower curvature convention differs from the upper comparison used in a CAT(0) space. A complete Riemannian manifold with sectional curvature at least is an example.