Geometry & Topology Seminar

Friday, September 18, 2020 2:30 pm - 2:30 pm EDT (GMT -04:00)

Chao Li, Princeton University

"Geometric comparison theorems for scalar curvature lower bounds"

In 2013, Gromov proposed a geometric comparison theorem for metrics with nonnegative scalar curvature, formulated in terms of the dihedral rigidity phenomenon for Riemannian polyhedrons: if a Riemannian polyhedron has nonnegative scalar curvature in the interior, and weakly mean convex faces, then the dihedral angle between adjacent faces cannot be everywhere less than the corresponding Euclidean model. In this talk, I will prove this conjecture for a large collection of polytopes, and extend it to metrics with negative scalar curvature lower bounds. The strategy is to relate this question with a geometric variational problem of capillary type, and apply the Schoen-Yau minimal slicing technique for manifolds with boundary. 

Zoom meeting: