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arXiv · 2505.17559

Critical Exponent Rigidity for $Θ-$positive Representations

Zhufeng Yao
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Abstract

We prove for a $Θ-$positive representation from a discrete subgroup $Γ\subset \mathsf{PSL}(2,\mathbb{R})$, the critical exponent for any $α\in Θ$ is not greater than one. When $Γ$ is geometrically finite, the equality holds if and only if $Γ$ is a lattice.

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Zhufeng Yao. 2026-02-06. Critical Exponent Rigidity for $Θ-$positive Representations. https://arxiv.org/abs/2505.17559

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