• Korean Journal of Mathematics
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• v.30 no.2
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• pp.315-333
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• 2022

We give a general procedure to analyze the structure for certain ℂ-Fuchsian subgroups of some non-arithmetic lattices. We also show their presentations and describe their fundamental domains which lie in a complex geodesic, a set homeomorphic to the unit disk.

• Bulletin of the Korean Mathematical Society
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• v.38 no.1
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• pp.211-222
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• 2001

In this paper, we prove the existence and uniqueness of a $\delta(\Gamma)$-conformal density on the limit set of $\Gamma$ acting on visibility manifold H for a Fuchsian group $\Gamma$.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.825-829
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• 1996

We prove that if G is the fundamental group of a closed surface or a Seifert fibered space and K is a finitely generated subgroup of G, and if for any element g in G there exists an integer $n_g$ such that $g^{n_g}$ belongs to K, then K is of finite index in G.

• Journal of the Korean Mathematical Society
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• v.55 no.3
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• pp.507-530
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• 2018

It is shown that for a non-unitary twist of a Fuchsian group, which is unitary at the cusps, Eisenstein series converge in some half-plane. It is shown that invariant integral operators provide a spectral decomposition of the space of cusp forms and that Eisenstein series admit a meromorphic continuation.