8 papers
Measurable boundary maps and Patterson--Sullivan measures for non-Borel Anosov groups on the Furstenberg boundary
Dongryul M. Kim, Andrew Zimmer
In this paper we develop a theory for Patterson--Sullivan measures for non-Borel Anosov groups on the Furstenberg boundary. Previously, such a theory has been successfully develope…
Vector-valued horofunction boundaries and Patterson--Sullivan measures
Dongryul M. Kim, Andrew Zimmer
In higher rank, there is a well-studied theory of Patterson--Sullivan measures supported on partial flag manifolds. However, establishing the existence and uniqueness of such measu…
Igusa Stacks and the Cohomology of Shimura Varieties II
Patrick Daniels, Pol van Hoften, Dongryul Kim +1
We construct Igusa stacks for all Shimura varieties of abelian type and derive consequences for the cohomology of these Shimura varieties. As an application, we prove that the Farg…
Invariant measures on the space of measured laminations for subgroups of mapping class group
Inhyeok Choi, Dongryul M. Kim
For a non-elementary subgroup of the mapping class group of a surface, we study its invariant Radon measures on the space of measured laminations, by classifying them on the recurr…
Classification of horospherical invariant measures in higher rank: Teaser
Inhyeok Choi, Dongryul M. Kim
This is an expository/teaser version of [arXiv:2601.22668] for a very special case of products of spaces. We keep this on arXiv as many parts of the argument of…
A note on the singularity conjecture for infinite covolume discrete subgroups
Dongryul M. Kim, Andrew Zimmer
We consider random walks on semisimple Lie groups where the support of the step distribution generates (as a group) a Zariski dense discrete subgroup of infinite covolume. When the…
Rigidity for Patterson--Sullivan systems with applications to random walks and entropy rigidity
Dongryul M. Kim, Andrew Zimmer
In this paper we introduce Patterson--Sullivan systems, which consist of a group action on a compact metrizable space and a quasi-invariant measure which behaves like a classical P…
Horocycles in hyperbolic 3-manifolds with round Sierpiński limit sets
Dongryul M. Kim, Minju Lee
Let M be a geometrically finite hyperbolic 3-manifold whose limit set is a round Sierpiński gasket, i.e. M is geometrically finite and acylindrical with a compact, totally geodesic…