Simone Cecchini, Texas A & M University

Title: Lipschitz rigidity for scalar curvature

Abstract: Let M be a closed connected smooth spin manifold of even dimension n, let g be a Riemannian metric of regularity W{1,p}, p > n, on M whose distributional scalar curvature in the sense of Lee-LeFloch is bounded below by n(n-1), and let f be a 1-Lipschitz continuous map of non-zero degree from (M,g) to the standard round n-sphere. Then f is a metric isometry. This generalizes a result of Llarull (1998) and answers a question of Gromov (2019) in his "four lectures".

This is joint work with Bernhard Hanke and Thomas Schick.