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.

Locations

• Symmetry Integrability and Geometry Methods and Applications - View - PDF
• arXiv (Cornell University) - View - PDF
• OPUS (Augsburg University) - View - PDF