7 papers
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…
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…
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…
Compactness of sequences of warped product circles over spheres with nonnegative scalar curvature
Wenchuan Tian, Changliang Wang
Gromov and Sormani conjectured that a sequence of three dimensional Riemannian manifolds with nonnegative scalar curvature and some additional uniform geometric bounds should have…
An Extreme Limit with Nonnegative Scalar Curvature
Christina Sormani, Wenchuan Tian, Changliang Wang
In 2014, Gromov vaguely conjectured that a sequence of manifolds with nonnegative scalar curvature should have a subsequence which converges in some weak sense to a limit space wit…
On a family of integral operators on the ball
Wenchuan Tian
In this work, we transform the equation in the upper half space first studied by Caffarelli and Silvestre to an equation in the Euclidean unit ball . We identify the…
A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature
Jiewon Park, Wenchuan Tian, Changliang Wang
Gromov and Sormani conjectured that sequences of compact Riemannian manifolds with nonnegative scalar curvature and area of minimal surfaces bounded below should have subsequences…