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.