Acta Mathematica Hungarica

, Volume 155, Issue 1, pp 3–24 | Cite as

Intersection probabilities and kinematic formulas for polyhedral cones

  • R. Schneider


For polyhedral convex cones in \({\mathbb{R}^d}\), we give a proof for the conic kinematic formula for conic curvature measures, which avoids the use of characterization theorems. For the random cones defined as typical cones of an isotropic random central hyperplane arrangement, we find probabilities for non-trivial intersection, either with a fixed cone, or for two independent random cones of this type.

Key words and phrases

polyhedral cone conic curvature measure kinematic formula intersection probability central hyperplane arrangement 

Mathematics Subject Classification

primary 52A22 secondary 52A55 


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Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2018

Authors and Affiliations

  1. 1.Mathematisches InstitutAlbert-Ludwigs-UniversitätFreiburg i. Br.Germany

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