11 papers
Torus and Positive Mass stability for metrics with Ricci curvature lower bound
Edward Bryden, Zhizhang Xie
Consider a sequence of metrics on the torus whose members have uniform lower bounds on their first stable systoles and Ricci curvatures, and have a uniform upper bound on the…
Gromov's dihedral rigidity conjecture in dimension three
Jinmin Wang, Zhizhang Xie, Guoliang Yu
In this article, we present a self-contained proof of Gromov's dihedral rigidity conjecture on scalar curvature in the three-dimensional case. The proof avoids many of the technica…
-metrics on tori and Schoen's conjecture
Jian Wang, Jinmin Wang, Zhizhang Xie
We prove Schoen's conjecture on -metrics for tori under an additional assumption on the fundamental group of the singular set. More precisely, we consider an -m…
Scalar curvature rigidity of spheres with subsets removed and metrics
Jinmin Wang, Zhizhang Xie
We prove the scalar curvature rigidity for metrics on , where is the -dimensional sphere with and is a closed su…
Scalar-mean rigidity beyond warped product spaces
Jinmin Wang, Zhizhang Xie
The main scalar-mean extremality and rigidity results in the existing literature concern manifolds whose curvature operators are nonnegative, or warped product spaces with a log-co…
Dihedral rigidity for submanifolds of warped product manifolds
Jinmin Wang, Zhizhang Xie
In this paper, we prove a dihedral extremality and rigidity theorem for a large class of codimension zero submanifolds with polyhedral boundary in warped product manifolds. We rema…