7 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…
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…
Zariski dense non-tempered subgroups in higher rank of nearly optimal growth
Mikolaj Fraczyk, Hee Oh
We construct the first example of a Zariski-dense, discrete, non-lattice subgroup of a higher rank simple Lie group , which is non-tempered in the sense that the quasi-reg…
Relatively Anosov groups: finiteness, measure of maximal entropy, and reparameterization
Dongryul M. Kim, Hee Oh
For a geometrically finite Kleinian group , the Bowen-Margulis-Sullivan measure is finite and is the unique measure of maximal entropy for the geodesic flow, as shown by Sulliva…
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,…
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 acting on a homogeneous space or, more generall…
Properly discontinuous actions, growth indicators, and conformal measures for transverse subgroups
Dongryul M. Kim, Hee Oh, Yahui Wang
Let be a connected semisimple real algebraic group. The class of transverse subgroups of includes all discrete subgroups of rank one Lie groups and any subgroups of Anosov…