Polar decomposition and Brion's theorem

Christian Haase

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arXiv · math/0312095

Polar decomposition and Brion's theorem

Christian Haase

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Abstract

In this note we point out the relation between Brion's formula for the lattice point generating function of a convex polytope in terms of the vertex cones [Brion1988] on the one hand, and the polar decomposition à la Lawrence/Varchenko [Lawrence1991, Varchenko1987] on the other. We then go on to prove a version of polar decomposition for non-simple polytopes.

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Christian Haase. 2004-06-10. Polar decomposition and Brion's theorem. https://arxiv.org/abs/math/0312095

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