59 citations · 264 across the 46 of their papers we have counts for
48 papers
-higher index, -higher rho invariant and cyclic cohomology
Jinmin Wang, Zhizhang Xie, Guoliang Yu
In this paper, we study -higher index theory and its pairing with cyclic cohomology for both closed manifolds and compact manifolds with boundary. We first give a sufficient g…
Covering complexity, scalar curvature, and quantitative -theory
Hao Guo, Guoliang Yu
We establish a relationship between a certain notion of covering complexity of a Riemannian spin manifold and positive lower bounds on its scalar curvature. This makes use of a pai…
On Gromov's compactness question regarding positive scalar curvature
Shmuel Weinberger, Zhizhang Xie, Guoliang Yu
In this paper, we give both positive and negative answers to Gromov's compactness question regarding positive scalar curvature metrics on noncompact manifolds. First we construct e…
On Gromov's dihedral extremality and rigidity conjectures
Jinmin Wang, Zhizhang Xie, Guoliang Yu
In this paper, we develop a new index theory for manifolds with polyhedral boundary. As an application, we prove Gromov's dihedral extremality conjecture regarding comparisons of s…
-theory of relative group -algebras and the relative Novikov conjecture
Jintao Deng, Geng Tian, Zhizhang Xie +1
The relative Novikov conjecture states that the relative higher signatures of manifolds with boundary are invariant under orientation-preserving homotopy equivalences of pairs. In…
A proof of Gromov's cube inequality on scalar curvature
Jinmin Wang, Zhizhang Xie, Guoliang Yu
Gromov proved a cube inequality on the bound of distances between opposite faces of a cube equipped with a positive scalar curvature metric in dimension using minimal surf…