19 citations · 111 across the 40 of their papers we have counts for
5 papers · 2 filters
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…
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…
A quantitative relative index theorem and Gromov's conjectures on positive scalar curvature
Zhizhang Xie
In this paper, we prove a quantitative relative index theorem. It provides a conceptual framework for studying some conjectures and open questions of Gromov on positive scalar curv…
Decay of scalar curvature on uniformly contractible manifolds with finite asymptotic dimension
Jinmin Wang, Zhizhang Xie, Guoliang Yu
Gromov proved a quadratic decay inequality of scalar curvature for a class of complete manifolds. In this paper, we prove that for any uniformly contractible manifold with finite a…