Intrinsic Volumes of Polyhedral Cones : A Combinatorial Perspective
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
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Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 371-409 |
| Journal / Publication | Discrete and Computational Geometry |
| Volume | 58 |
| Issue number | 2 |
| Online published | 5 Jul 2017 |
| Publication status | Published - Sept 2017 |
Link(s)
| DOI | DOI |
|---|---|
| Attachment(s) | Documents
Publisher's Copyright Statement
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| Link to Scopus | https://www.scopus.com/record/display.uri?eid=2-s2.0-85021832561&origin=recordpage |
| Permanent Link | https://scholars.cityu.edu.hk/en/publications/publication(b15d2a8b-d352-4ccb-b706-3c445f0f997c).html |
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.
Research Area(s)
- Geometric probability, Hyperplane arrangements, Integral geometry, Intrinsic volumes, Polyhedral cones
Citation Format(s)
Intrinsic Volumes of Polyhedral Cones: A Combinatorial Perspective. / Amelunxen, Dennis; Lotz, Martin.
In: Discrete and Computational Geometry, Vol. 58, No. 2, 09.2017, p. 371-409.
In: Discrete and Computational Geometry, Vol. 58, No. 2, 09.2017, p. 371-409.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
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