Professor Fu will study possible analogs of scalar-valued curvatures on singular spaces. The principal investigator has already made some progress in this direction and will try to extend his work from special cases to more general singular spaces. The primary method to be used in the investigation is geometric measure theory. One of the goals of this research is to understand how classical invariants of geometry such as curvature can be extended to singular spaces, that is, spaces with corners, cusps, or self intersections. These classical invariants are very important in our understanding of the geometry of a space and the extension of these concepts to singular spaces, which are playing an increasingly central role in the modeling of physical systems, should have immediate application.
