Scalar curvature rigidity of warped product metrics

Autoren: Christian Bär, Simon Brendle, Bernhard Hanke, Yipeng Wang (2024)

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 minus two antipodal points, thus resolving a problem in Gromov's  ``Four Lectures'' in all dimensions. 

Our arguments are based on spin geometry.

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
article 035, 26 pages

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