Geometric measures for random mosaics in spherical spaces
E. Arbeiter, Martina Zähle · Stochastics and stochastics reports · 1994
This paper deals with isotropic random mosaics of S d-1whose cells are piecewise smooth. As geometric measures concentrated on the i-skeleton the i-dimensional surface area (volume) measure and (i — 1) different curvature measures are chosen. Relations between the corresponding densities are found. This leads to a parameter system from which all mean values can be calculated. The curvature intensities are also computed for the intersection with a subsphere, for superposition and for great hypersphere mosaics.