12 citations · 13 across the 15 of their papers we have counts for
15 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 h…
Groups Generated by Root Unipotents: Higher-rank and rank-one
Yanlong Hao
For , let \[ Γ(Q)=\langle E_{ij}(q_{ij}):i\neq j\rangle \] be the subgroup of generated by elementary matrices with nonzero rational param…
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 . In…
Marked length varieties and arithmeticity
Yanlong Hao
This paper gives an example of a non-arithmetic surface with marked length variety rigidity.
Arithmeticity and geometrical commensurators
Yanlong Hao
We establish a coarse-geometric analogue of Margulis's commensurator criterion for groups acting on good Gromov-hyperbolic spaces. For a non-elementary -lattice ,…
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…
Marked length spectra of Gromov hyperbolic space
Yanlong Hao
Let , be two roughly geodesically complete Gromov hyperbolic spaces under comparable isometric actions of . Assume that the limit set .…
Bounded clustering property characterizes arithmetic nonuniform Kleinian groups
Yanlong Hao
In this short note, we show that the B-C property characterizes arithmetic lattices along all nonuniform lattices in .
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…
The homotopy fixed point sets of spheres actions on rational complexes
Yanlong Hao, Xiugui Liu, Qianwen Sun
In this paper, we describe the homotopy type of the homotopy fixed point sets of -actions on rational spheres and complex projective spaces, and provide some properties of $S^…
On the rational homotopical nilpotency index of principal bundles
Yanlong Hao, Xiugui Liu
Let denote the space of all self-fibre homotopy equivalences of a principal -bundle of simply connected CW complexes with finite. When …
Two-stage spaces and the torus rank conjecture
Yanlong Hao, Xiugui Liu, Qianwen Sun
In this note, we give some new families of two-stage spaces for which the torus rank conjecture is affirmed.
Marked length pattern rigidity for arithmetic manifolds
Yanlong Hao
In this paper, we prove a cocycle version of marked length spectrum rigidity. There are two consequences. The first is marked length pattern rigidity for arithmetic hyperbolic loca…
Models in Rational homotopy theory and Torus Rank Conjecture
Yanlong Hao, Xiugui Liu, Qianwen Sun
In this paper, we focus on some models in rational homotopy theory, Sullivan model, Quillen model, C_\infty model, and L_\infty model. We give some connections between them. As an…
Moore's Conjecture for Polyhedral Products
Yanlong Hao, Qianwen Sun, Stephen Theriault
Moore's Conjecture is shown to hold for generalized moment-angle complexes and a criterion is proved that determines when a polyhedral product is elliptic or hyperbolic.