Critical Exponent Rigidity for $\Theta-$positive Representations

Zhufeng Yao

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arXiv · 2505.17559

Critical Exponent Rigidity for $\Theta-$positive Representations

Zhufeng Yao

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Abstract

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

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Zhufeng Yao. 2025-05-23. Critical Exponent Rigidity for $\Theta-$positive Representations. https://arxiv.org/abs/2505.17559

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