## Student Geometry/Topology

•  Wenchuan Tian
•  A Compactness Theorem for Rotationally Symmetric Riemannian Manifolds with Positive Scalar Curvature
•  10/31/2018
•  4:10 PM - 5:00 PM
•  A202 Wells Hall

Gromov conjectured that sequences of compact Riemannian manifolds with positive scalar curvature should have subsequences which converge in the intrinsic flat sense to limit spaces with some generalized notion of scalar curvature. In light of three dimensional examples discovered jointly with Basilio and Dodziuk, Sormani suggested that one add an hypothesis assuming a uniform lower bound on the area of a closed minimal surface. We have proven this revised conjecture in the setting where the sequence of manifolds are 3 dimensional rotationally symmetric warped product manifolds. This is a project given by professor Christina Sormani, and is joint work with Jiewon Park and Changliang Wang.

## Contact

Department of Mathematics
Michigan State University