Geodesic
Scalar Curvature Rigidity of Warped Product Metrics
Symmetry, integrability and geometry: methods and applications, Tome 20 (2024) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: scalar curvature, warped product, bandwidth estimate, Llarull's theorem, holographic index theorem. 
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     author = {Christian B\"ar and Simon Brendle and Bernhard Hanke and Yipeng Wang},
     title = {Scalar {Curvature} {Rigidity} of {Warped} {Product} {Metrics}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2024},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a34/}
}
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Christian Bär; Simon Brendle; Bernhard Hanke; Yipeng Wang. Scalar Curvature Rigidity of Warped Product Metrics. Symmetry, integrability and geometry: methods and applications, Tome 20 (2024). http://geodesic.mathdoc.fr/item/SIGMA_2024_20_a34/

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