3 papers
math.MG2025
Geometric Convergence to an Extreme Limit Space with nonnegative scalar curvature
Christina Sormani, Wenchuan Tian, Wai-Ho Yeung
In 2014, Gromov conjectured that sequences of manifolds with nonnegative scalar curvature should have subsequences which converge in some geometric sense to limit spaces with some…
math.DG2024
More Extreme Limits of Manifolds with Positive Scalar Curvature
Wenchuan Tian
In this article, we extend the example constructed in the paper by Sormani-Tian-Wang to build new examples that satisfy the assumptions of the conjecture by Gromov. Each of these n…
math.DG2024
On the Scalar Curvature Compactness Conjecture in the Conformal Case
Brian Allen, Wenchuan Tian, Changliang Wang
Is a sequence of Riemannian manifolds with positive scalar curvature, satisfying some conditions to keep the sequence reasonable, compact? What topology should one use for the conv…