Entropy degeneration of convex projective surfaces

Abstract

We show that the volume entropy of the Hilbert metric on a closed convex projective surface tends to zero as the corresponding Pick differential tends to infinity. The proof is based on the theorem, due to Benoist and Hulin, that the Hilbert metric and Blaschke metric are comparable.

5 pages

References in corpus (1)

• Meromorphic cubic differentials and convex projective structures

Cited by in corpus (5)

• Currents, Systoles, and Compactifications of Character Varieties
• Entropy of Hilbert metrics and length spectrum of Hitchin representations in $\mathrm{PSL}(3,\mathbb{R})$
• Convex RP^2 Structures and Cubic Differentials under Neck Separation
• Minimal surfaces for Hitchin representations
• Length spectrum compactification of the ${\mathrm{SO}}_0(2,3)$-Hitchin component