The shape of parallel surfaces: porous media, fluctuating interfaces and complex fluids

The morphological concept of parallel surfaces in combination with curvature measures known from integral geometry are used to characterise and model complex spatial structures beyond the two-point correlation function and to predict, for instance, percolation thresholds in porous media. Applied to liquid interfaces one finds a reduction of the surface tension at microscopic scales in good agreement with X-ray scattering experiments.