Conical Singularity

A point of a manifold or metric space at which the neighborhood is locally isometric (or homeomorphic with compatible metric structure) to a metric cone over some base space; geometrically it appears as a 'tip' where the usual Euclidean structure fails and angular or radial metrics exhibit cone-like behavior.

A point-like boundary singularity occurring at a cone tip or vertex where local geometry is modeled by a product of a radial variable and a compact link (the cone cross-section), and where solutions exhibit asymptotics determined by the spectral problem on that link.