From the 1 of 7 linked papers with an AI index.
7 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…
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…
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,…
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…
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-re…
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 Sulliv…