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Daniel Hug Rolf Schneider We consider a stationary Poisson hyperplane process with given directional distribution and intensity in $d$-dimensional Euclidean space.
DANIEL HUG and ROLF SCHNEIDER. Dedicated to Tudor Zamfirescu on the occasion of his sixtieth birthday. It is proved that the shape of the typical cell of a Poisson–Delaunay tessel-lation of Rd tends to the shape of a regular simplex, given that the surface area, or the inradius, or the minimal width, of the typical cell tends to in-finity.
Daniel Hug and Rolf Schneider Abstract The intrinsic volumes, recalled in the previous chapter, provide an array of size measurements for a convex body, one for each integer degree of homogeneity from 0 to n. For measurements and descriptions of other aspects, such as position,
Daniel Hug Valuations, Integral Geometry and Linear Dependences • Objects of integral geometry. Let En k be the Grassmannian of k-flats in Rn, let µn k be a Haar measure on E n k. Then, for K∈ Kn and 0 6 j6 k6 n, we have the Crofton formula Z En k Vj(K∩E)µn k(dE) = αnjkVn+j−k(K). Let G(n) be the motion group, and µa Haar measure on ...
LARGE TYPICAL CELLS IN POISSON–DELAUNAY MOSAICS DANIEL HUG and ROLF SCHNEIDER Dedicated to Tudor Zamfirescu on the occasion of his sixtieth birthday. Published 2005. Mathematics.
Daniel Hug and Rolf Schneider. Abstract. The support measures of a convex body are a common generalization of the curvature measures and the area measures. With respect to the Hausdorff metric on the space of convex bodies, they are weakly continuous.
Then we investigate how the shapes of the faces are influenced by assumptions of different types: either via containment of convex bodies of given volume (including a new result for k = d ), or, for weighted typical k -faces, in the spirit of D. G. Kendall's asymptotic problem, suitably generalized.
