On the Hilbert geometry of simplicial Tits sets

Abstract

The moduli space of convex projective structures on a simplicial hyperbolic Coxeter orbifold is either a point or the real line. Answering a question of M. Crampon, we prove that in the latter case, when one goes to infinity in the moduli space, the entropy of the Hilbert metric tends to 0.

arXiv comment18 pages, 5 figures

References in corpus (1)

• The degeneration of convex RP^2 structures on surfaces

Cited by in corpus (4)

• Degeneration of Hitchin representations along internal sequences
• Entropy degeneration of convex projective surfaces
• Correlation of the renormalized Hilbert length for convex projective surfaces
• Limit polygons of convex domains in the projective plane