10 papers
Strict concavity of the growth indicator function for relatively Anosov groups
Dongryul M. Kim, Hee Oh, Andrew Zimmer
Let be a discrete subgroup of a connected semisimple real algebraic group of higher rank. The growth indicator function records the directional exponential growth of the…
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…
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…
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…
Weakly holomorphic homogeneous regular manifolds
Andrew Zimmer
We introduce a class of complex manifolds which we call weakly holomorphic homogeneous regular manifolds (wHHR) manifolds. As the name suggests, this class contains the so-called h…
Smooth equivalence of families of strongly pseudoconvex domains
Hervé Gaussier, Xianghong Gong, Andrew Zimmer
We establish a smoothness result for families of biholomorphisms between smooth families of strongly pseudoconvex domains, each with trivial biholomorphism group. This is accomplis…
The structure of relatively hyperbolic groups in convex real projective geometry
Mitul Islam, Andrew Zimmer
In this paper we prove a general structure theorem for relatively hyperbolic groups (with arbitrary peripheral subgroups) acting naive convex co-compactly on properly convex domain…