7 papers
On the length sets of closed hyperbolic surfaces
Yanlong Hao
For every closed surface of genus , we prove that there exists a countable union of positive-codimension algebraic subsets of Teichmüller space such that, for every…
Groups Generated by Root Unipotents: Higher-rank and rank-one
Yanlong Hao
We study subgroups generated by prescribed unipotent elements. For , let \[ Î(Q)=\langle E_{ij}(q_{ij}):i\neq j\rangle \] be the subgroup of $\operatorname{SL}(n,\mathbb…
Marked length varieties and arithmeticity
Yanlong Hao
This paper gives an example of a non-arithmetic surface with marked length variety rigidity.
Brownian motion and orbit counting of Kleinian groups
Yanlong Hao, Beibei Liu
In this paper, we investigate the relationship between the divergence of Kleinian groups and the recurrence of simple random walks on the Schreier graph associated with .…
On trace set of hyperbolic surfaces and a conjecture of Sarnak and Schmutz
Yanlong Hao
In this paper, we investigate the trace set of a Fuchsian lattice. There are two results of this paper: the first is that for a non-uniform lattice, we prove Scmutz's conjecture: t…
Groups that (do not) act isometrically on hyperbolic spaces
Yanlong Hao
In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on so…