Applications of Minkowski Functionals to the Statistical Analysis of Dark Matter Models

A new method for the statistical analysis of 3D point processes, based on the family of Minkowski functionals, is explained and applied to modelled galaxy distributions generated by a toy-model and cosmological simulations of the large-scale structure in the Universe. These measures are sensitive to both, geometrical and topological properties of spatial patterns and appear to be very effective in discriminating different point processes. Moreover by the means of conditional subsampling, different building blocks of large-scale structures like sheets, filaments and clusters can be detected and extracted from a given distribution.Comment: 13 pages, Latex, 2 gzipped tar-files, to appear in: Proc. ``1st SFB workshop on Astro-particle physics'', Ringberg, Tegernsee, 199