Author

Dongryul M. Kim

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Preprint Sep 2026

Extremal entropy for products of Fuchsian representations

In this paper, we count the number of (almost) extremally stretched closed geodesics for a pair of (non-conjugate) Fuchsian representations of a closed surface group, and show that it has subexponential growth. We then deduce that, as a discrete subgroup of $\mathsf{PO}(2, 1) \times \mathsf{PO}(2, 1)$, the growth indic...

Richard D. Canary, Dongryul M. Kim · 0 citations

Preprint Oct 2026

Higher-rank local mixing for cusped positive representations

Let $\Gamma<\operatorname{PSL}_2(\mathbb R)$ be a torsion-free, non-elementary, finitely generated Fuchsian group with parabolic elements, and let $\rho:\Gamma\to G$ be a type-preserving, Zariski dense, positive representation into a connected split semisimple real algebraic group. We prove quantitative local mixing fo...

Dongryul M. Kim, Hee Oh, Wen-Yu Pan · 0 citations