Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective

Amelunxen, Dennis and Lotz, Martin (2015) Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective. [MIMS Preprint]

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Abstract

These notes provide a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Streamlined derivations of the General Steiner formula, the conic analogues of the Brianchon-Gram-Euler and the Gauss-Bonnet relations, and the Principal Kinematic Formula are given. In addition, a connection between the characteristic polynomial of a hyperplane arrangement and the intrinsic volumes of the regions of the arrangement, due to Klivans and Swartz, is generalized and some applications presented.

Item Type: MIMS Preprint
Uncontrolled Keywords: Convex geometry, polyhedra, cones, intrinsic volumes, integral geometry, geometric probability, kinematic formula, Gauss-Bonnet, hyperplane arrangements
Subjects: MSC 2010, the AMS's Mathematics Subject Classification > 52 Convex and discrete geometry
MSC 2010, the AMS's Mathematics Subject Classification > 60 Probability theory and stochastic processes
Depositing User: Dr. Martin Lotz
Date Deposited: 19 Dec 2015
Last Modified: 08 Nov 2017 18:18
URI: http://eprints.maths.manchester.ac.uk/id/eprint/2423

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