9 papers
Riemannian Positive Mass Theorem in All Dimensions in the Presence of Low-Codimension Singularities
Marcus Khuri, Jian Wang, Jinmin Wang
We prove the Riemannian positive mass theorem in all dimensions for asymptotically flat -metrics with subcritical singular sets. More precisely, we consider complete asym…
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, sharp bottom spectrum and geometric rigidity
Jinmin Wang, Bo Zhu
We prove rigidity in the equality case of the sharp bottom spectrum estimate under scalar curvature lower bound. Under the same topological assumptions as in our previous work, a c…
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…