13 citations · 32 across the 13 of their papers we have counts for
13 papers
Actions on CAT(-1) spaces with critical exponent less than 1
Beibei Liu, Shi Wang
We show that for a discrete isometry subgroup acting on a proper CAT(-1) space X, if the critical exponent is less than , then the critical exponent equals the Hausdorff dimensi…
The natural flow and the critical exponent
Chris Connell, D. B. McReynolds, Shi Wang
Inspired by work of Besson-Courtois-Gallot, we construct a flow called the natural flow on a non-positively curved Riemannian manifold . As with the natural map, the -Jacobia…
Marked length spectrum rigidity for relatively hyperbolic groups
Thang Nguyen, Shi Wang
We consider a coarse version of the marked length spectrum rigidity: given a group with two left invariant metrics, if the marked length spectrum (the translation length function)…
An -norm-mass inequality for complete manifolds
Caterina Campagnolo, Shi Wang
We generalize an inequality of Besson-Courtois-Gallot about volume and simplicial volume of closed manifolds to the -norm of all the homology classes of complete manifolds.…
Cusps, Kleinian groups and Eisenstein series
Beibei Liu, Shi Wang
We study the Eisenstein series associated to the full rank cusps in a complete hyperbolic manifold. We show that given a Kleinian group , each full…
Geometric cycles and bounded cohomology for a cocompact lattice in
Shi Wang
We show there exists a closed locally symmetric manifold modeled on , and a non-trivial homology class in degree represented by a totall…
Discrete subgroups of small critical exponent
Beibei Liu, Shi Wang
We prove that finitely generated higher dimensional Kleinian groups with small critical exponent are always convex-cocompact. Along the way, we also prove some geometric properties…
Cheeger-Gromoll Splitting Theorem for groups
Thang Nguyen, Shi Wang
We study a notion of curvature for finitely generated groups which serves as a role of Ricci curvature for Riemannian manifolds. We prove an analog of Cheeger-Gromoll splitting the…
Homological norms on nonpositively curved manifolds
Chris Connell, Shi Wang
We relate the Gromov norm on homology classes to the harmonic norm on the dual cohomology and obtain double sided bounds in terms of the volume and other geometric quantities of th…
Some remarks on the simplicial volume of nonpositively curved manifolds
Chris Connell, Shi Wang
We show that any closed manifold with a metric of nonpositive curvature that admits either a single point rank condition or a single point curvature condition has positive simplici…
Positivity of Simplicial Volume for Nonpositively Curved Manifolds with a Ricci-type curvature condition
Chris Connell, Shi Wang
We show that closed manifolds supporting a nonpositively curved metric with negative -Ricci curvature, have positive simplicial volume. This answers a special ca…
On splitting rank of non-compact type symmetric spaces and bounded cohomology
Shi Wang
Let be a higher rank symmetric space of non-compact type, where is the connected component of the isometry group of . We define the splitting rank of , denoted by…
Barycentric straightening and bounded cohomology
Jean-François Lafont, Shi Wang
We study the barycentric straightening of simplices in irreducible symmetric spaces of non-compact type. We show that, for an n-dimensional symmetric space of rank r>1, the p-Jacob…