From the 1 of 8 linked papers with an AI index.
8 papers
Strict concavity of the growth indicator function for relatively Anosov groups
Dongryul M. Kim, Hee Oh, Andrew Zimmer
The paper proves that for non‑elementary relatively Anosov subgroups of higher‑rank semisimple Lie groups, the growth indicator function is strictly concave in non‑collinear direct…
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…
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…
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…
Rigidity of proper holomorphic maps between balls with Hölder boundary regularity
Kyle Huang, Jinwoo Park, Aleksander Skenderi +3
In this paper, we prove a rigidity result for proper holomorphic maps between unit balls that have many symmetries and which extend to Hölder continuous maps on the boundary, with…