Scalar curvature rigidity of warped product metrics

Abstract

We show scalar-mean curvature rigidity of warped products of round spheres of dimension at least 2 over compact intervals equipped with strictly log-concave warping functions. This generalizes earlier results of Cecchini-Zeidler to all dimensions. Moreover, we show scalar curvature rigidity of round spheres of dimension at least 3 with two antipodal points removed. This resolves a problem in Gromov's ''Four Lectures'' in all dimensions. Our arguments are based on spin geometry.

published version

References in corpus (2)

• Rigidity of 3D spherical caps via $\mu$-bubbles
• Scalar curvature rigidity of degenerate warped product spaces

Cited by in corpus (1)

• The degree condition in Llarull's theorem on scalar curvature rigidity