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- Daniel Hug, Rolf Schneider, S Chern, H Hadwiger
- 2004

The principal kinematic formula and the closely related Crofton formula are central themes of integral geometry in the sense of Blaschke and Santaló. There have been various generalizations , variants, and analogues of these formulae, in part motivated by applications. We give a survey of recent investigations in the spirit of the kinematic and Crofton… (More)

- Károly J Böröczky, Rolf Schneider
- 2007

We characterize the duality of convex bodies in d-dimensional Euclidean vector space, viewed as a mapping from the space of convex bodies containing the origin in the interior into the same space. The question for such a characterization was posed by Vitali Milman. Sufficient for a characterization, up to a trivial exception and the composition with a… (More)

- K Aroly, Or¨oczky And, Rolf Schneider
- 2008

For a given convex body K in R d , a random polytope K (n) is defined (essentially) as the intersection of n independent closed halfspaces containing K and having an isotropic and (in a specified sense) uniform distribution. We prove upper and lower bounds, of optimal orders, for the difference of the mean widths of K (n) and K, as n tends to infinity. For… (More)

- Juan Jose Martin, Ingrid Hausser, Philippe Lyrer, Otto Busse, Ralf Schwarz, Rolf Schneider +5 others
- Stroke
- 2006

BACKGROUND AND PURPOSE
Genetic risk factors are thought to play a role in the etiology of spontaneous cervical artery dissections (CAD). However, familial CAD is extremely rare. In this study we analyzed patients with familial CAD and asked the question whether familial CAD has particular features.
METHODS
Seven families with 15 CAD patients were… (More)

We study asymptotic properties of the approximation of a suuciently smooth convex body K in R d by the convex hulls of n points in the boundary of K, for n ! 1. The deviation is measured by the Hausdorr distance. The asymptotic distribution of the vertices of best-approximating polytopes is determined. Further results involve prescribed densities for the… (More)

It is proved that the shape of the typical cell of a Delaunay tessellation, derived from a stationary Poisson point process in d-dimensional Euclidean space, tends to the shape of a regular simplex, given that the volume of the typical cell tends to infinity. This follows from an estimate for the probability that the typical cell deviates by a given amount… (More)