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: | https://eprints.maths.manchester.ac.uk/id/eprint/2423 |
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