8 papers · 1 filter
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…
A global shadow lemma for relatively Morse groups in higher rank
Dongryul M. Kim, Hee Oh
Patterson-Sullivan measures encode the distribution of orbits of discrete group actions near the boundary. In this paper, we prove a global shadow lemma for Patterson-Sullivan meas…
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…
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…
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…
Rigidity of Kleinian groups via self-joinings: measure theoretic criterion
Dongryul M. Kim, Hee Oh
Let . Let be a Zariski dense convex cocompact subgroup and be its limit set. Let be a…