185 research outputs found
Hilbert geometry of polytopes
It is shown that the Hilbert metric on the interior of a convex polytope is
bilipschitz to a normed vector space of the same dimension.Comment: 11 pages, minor changes, to appear in Archiv Mat
Generalized translation invariant valuations and the polytope algebra
We study the space of generalized translation invariant valuations on a
finite-dimensional vector space and construct a partial convolution which
extends the convolution of smooth translation invariant valuations. Our main
theorem is that McMullen's polytope algebra is a subalgebra of the (partial)
convolution algebra of generalized translation invariant valuations. More
precisely, we show that the polytope algebra embeds injectively into the space
of generalized translation invariant valuations and that for polytopes in
general position, the convolution is defined and corresponds to the product in
the polytope algebra.Comment: 29 pages; minor change
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