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arXiv · 2306.04015

Scalar curvature rigidity of warped product metrics

Christian Baer·Simon Brendle·Bernhard Hanke·Yipeng Wang
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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.

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Christian Baer, Simon Brendle, Bernhard Hanke, Yipeng Wang. 2023-06-06. Scalar curvature rigidity of warped product metrics. https://doi.org/10.3842/sigma.2024.035

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