Metadata
Abstract
We interpret the Hilbert entropy of a convex projective structure on a closed higher-genus surface as the Hausdorff dimension of the non-differentiability points of the limit set in the full flag space $\mathcal{F}(\mathbb{R}^3)$. Generalizations for regularity properties of boundary maps between locally conformal representations are also discussed. An ingredient for the proofs is the concept of hyperplane conicality that we introduce for a $\theta $-Anosov representation into a reductive real-algebraic Lie group $\mathsf {G}$. In contrast with directional conicality, hyperplane-conical points always have full mass for the corresponding Patterson–Sullivan measure.
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