Scalar curvature rigidity of warped product metrics
Differential Geometry
2024-04-19 v2
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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Cite
@article{arxiv.2306.04015,
title = {Scalar curvature rigidity of warped product metrics},
author = {Christian Baer and Simon Brendle and Bernhard Hanke and Yipeng Wang},
journal= {arXiv preprint arXiv:2306.04015},
year = {2024}
}
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