On the Hilbert geometry of simplicial Tits sets

Details On the Hilbert geometry of simplicial Tits sets On the Hilbert geometry of simplicial Tits sets

2011-11-05

arxiv.org/abs/1111.1288v1

Mathematics

Differential Geometry

20 pages, 5 figures

Scientific paper

The moduli space of convex projective structures on a hyperbolic simplicial
Coxeter orbifold is either a point or can be identified with the open half real
line. We study the Hilbert geometry on these orbifolds. In particular, we prove
that in the latter case, when one goes to 0 or infinity in the moduli space,
the entropy of geodesic flow tends to 0

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