University of Connecticut

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PDE and Differential Geometry Seminar
Positive scalar curvature and the dihedral rigidity conjecture
Chao Li (Princeton University)

Monday, September 9, 2019
2:30pm – 3:30pm

Storrs Campus
MONT 214

In 2013, Gromov proposed a dihedral rigidity conjecture, aiming at establishing a geometric comparison theory for metrics with positive scalar curvature. The conjecture states that 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. I will prove this conjecture for a large collection of polytopes. The strategy is to relate this conjecture with a geometric variational problem of capillary type, and apply the Schoen-Yau minimal slicing technique for manifolds with boundary.


PDE and Differential Geometry Seminar (primary), UConn Master Calendar

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