Dongryul M. Kim

activity

20162026

most cited50 Years of the Golomb--Welch Conjecture

19 citations · 49 across the 29 of their papers we have counts for

collaborators

31 papers

math.GT2026

Extremal entropy for products of Fuchsian representations

Richard Canary, Dongryul Kim

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…

math.DG2026

Strict concavity of the growth indicator function for relatively Anosov groups

Dongryul M. Kim, Hee Oh, Andrew Zimmer

Let $Γ$ be a discrete subgroup of a connected semisimple real algebraic group of higher rank. The growth indicator function $ψ_{Γ}$ records the directional exponential growth of the…

math.GT2026

Global shadow estimates and Hausdorff measure criteria in higher rank

Dongryul M. Kim, Hee Oh

Patterson--Sullivan measures encode the distribution of orbits of discrete group actions near the boundary. We prove a global shadow lemma for Patterson--Sullivan measures associat…

math.GT2026

Non-arithmeticity of length spectra of subgroups of mapping class groups

Inhyeok Choi, Dongryul M. Kim

In this paper, we prove that every non-elementary subgroup of the mapping class group of a surface has non-arithmetic Teichmüller length spectrum. Namely, Teichmüller translation l…

math.DS2026

Classification of horospherical invariant measures in higher rank: The Full Story

Inhyeok Choi, Dongryul M. Kim

In this paper, we classify horospherical invariant Radon measures for Anosov subgroups of arbitrary semisimple real algebraic groups. This generalizes the works of Burger and Robli…

math.GT2025

Determining subgroups via stationary measures

Dongryul M. Kim, Andrew Zimmer

In this paper, we consider random walks on the isometry groups of general metric spaces. Under some mild conditions, we show that if two non-elementary random walks on a discrete s…

math.NT2024★ 1 cited

Igusa Stacks and the Cohomology of Shimura Varieties

Patrick Daniels, Pol van Hoften, Dongryul Kim +1

We construct functorial Igusa stacks for all Hodge-type Shimura varieties, proving a conjecture of Scholze and extending earlier results of the fourth-named author for PEL-type Shi…

math.GT2024

Conformal measure rigidity and ergodicity of horospherical foliations

Dongryul M. Kim

In this paper, we prove two main theorems: conformal measure rigidity and ergodicity of horospherical foliations, especially in higher rank. Both theorems are new even for relative…

math.DS2024

Relatively Anosov groups: finiteness, measure of maximal entropy, and reparameterization

Dongryul M. Kim, Hee Oh

For a geometrically finite Kleinian group $Γ$ , the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sulliva…

math.NT2024★ 1 cited

On a conjecture of Pappas and Rapoport

Patrick Daniels, Pol van Hoften, Dongryul Kim +1

We prove a conjecture of Pappas and Rapoport about the existence of ''canonical'' integral models of Shimura varieties of Hodge type with quasi-parahoric level structure at a prime…

math.AC2024

Descending finite projective modules from a Novikov ring

Dongryul Kim

We prove a descent result for finite projective modules, motivated by a question in perfectoid geometry. Given a commutative ring $A$ , we formulate a descent problem for descending…

math.GR2024

Ahlfors regularity of Patterson-Sullivan measures of Anosov groups and applications

Subhadip Dey, Dongryul M. Kim, Hee Oh

For all Zarski dense Anosov subgroups of a semisimple real algebraic group, we prove that their limit sets are Ahlfors regular for intrinsic conformal premetrics. As a consequence,…

math.DS2023

Ergodic dichotomy for subspace flows in higher rank

Dongryul M. Kim, Hee Oh, Yahui Wang

In this paper, we study the ergodicity of a one-parameter diagonalizable subgroup of a connected semisimple real algebraic group $G$ acting on a homogeneous space or, more generall…

math.DS2023

Properly discontinuous actions, growth indicators, and conformal measures for transverse subgroups

Dongryul M. Kim, Hee Oh, Yahui Wang

Let $G$ be a connected semisimple real algebraic group. The class of transverse subgroups of $G$ includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov…

math.DS2023

Non-concentration property of Patterson-Sullivan measures for Anosov subgroups

Dongryul M. Kim, Hee Oh

Let $G$ be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup $Γ < G$ with respect to a parabolic subgroup $P_{θ}$ , we prove that any $Γ$ -Patterson-Sulliv…

math.DS2023★ 1 cited

Hausdorff dimension of directional limit sets for self-joinings of hyperbolic manifolds

Dongryul M. Kim, Yair Minsky, Hee Oh

The classical result of Patterson and Sullivan says that for a non-elementary convex cocompact subgroup $Γ < SO^{\circ} (n, 1)$ , $n \geq 2$ , the Hausdorff dimension of the limit se…

math.GT2023

Rigidity of Kleinian groups via self-joinings: measure theoretic criterion

Dongryul M. Kim, Hee Oh

Let $n, m \geq 2$ . Let $Γ < SO^{\circ} (n + 1, 1)$ be a Zariski dense convex cocompact subgroup and $Λ \subset S^{n}$ be its limit set. Let $ρ : Γ \to SO^{\circ} (m + 1, 1)$ be a…

math.GT2023★ 1 cited

Conformal measure rigidity for representations via self-joinings

Dongryul M. Kim, Hee Oh

Let $Γ$ be a Zariski dense discrete subgroup of a connected simple real algebraic group $G_{1}$ . We discuss a rigidity problem for discrete faithful representations $ρ : Γ \to G_{2}$ and…

math.GT2022

Rigidity of Kleinian groups via self-joinings

Dongryul M. Kim, Hee Oh

Let $Γ < PSL_{2} (C) ≃ Isom^{+} (H^{3})$ be a finitely generated non-Fuchsian Kleinian group whose ordinary set $Ω = S^{2} - Λ$ has at least two co…

math.GT2021

Reducible normal generators for mapping class groups are abundant

Hyungryul Baik, Dongryul M. Kim, Chenxi Wu

In this article, we study the normal generation of the mapping class group. We first show that a mapping class is a normal generator if its restriction on the invariant subsurface…

math.GT2021

Tent property of the growth indicator functions and applications

Dongryul M. Kim, Yair N. Minsky, Hee Oh

Let $Γ$ be a Zariski dense discrete subgroup of a connected semisimple real algebraic group $G$ . Let $k = rank G$ . Let $ψ_Γ:\mathfrak{a} \to \mathbb{R}\cup \{-\infty\}…

math.GT2021

Minimal asymptotic translation lengths on curve complexes and homology of mapping tori

Hyungryul Baik, Dongryul M. Kim, Chenxi Wu

Let $S_{g}$ be a closed orientable surface of genus $g > 1$ . Consider the minimal asymptotic translation length $L_{T} (k, g)$ on the Teichmüller space of $S_{g}$ , among pseud…

math.GT2021★ 1 cited

Linear growth of translation lengths of random isometries on Gromov hyperbolic spaces and Teichmüller spaces

Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim

We investigate the translation lengths of group elements that arise in random walks on the isometry groups of Gromov hyperbolic spaces. In particular, without any moment condition,…

math.GT2020★ 2 cited

Simple length spectra as moduli for hyperbolic surfaces and rigidity of length identities

Hyungryul Baik, Inhyeok Choi, Dongryul M. Kim

In this article, we revisit classical length identities enjoyed by simple closed curves on hyperbolic surfaces. We state and prove the rigidity of such identities over Teichmüller…