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arXiv · 1512.06033

Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective

Dennis Amelunxen·Martin Lotz
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Abstract

The theory of intrinsic volumes of convex cones has recently found striking applications in areas such as convex optimization and compressive sensing. This article provides a self-contained account of the combinatorial theory of intrinsic volumes for polyhedral cones. Direct 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 are presented.

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Dennis Amelunxen, Martin Lotz. 2017-08-22. Intrinsic Volumes of Polyhedral Cones: A combinatorial perspective. https://arxiv.org/abs/1512.06033

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