We consider analogs of the Lipschitz-Killing curvatures of smooth Riemannian manifolds for piecewise flat spaces. In the special case of scalar curvature, the definition is due to T. Regge; considerations in this spirit date back to J. Steiner. We show that if a piecewise flat space approximates a smooth space in a suitable sense, then the corresponding curvatures are close in the sense of measures.
|Original language||English (US)|
|Number of pages||50|
|Journal||Communications In Mathematical Physics|
|State||Published - Sep 1984|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics