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Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 035, 26 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.035 (Mi sigma2037) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Scalar Curvature Rigidity of Warped Product Metrics

Christian Bära, Simon Brendleb, Bernhard Hankec, Yipeng Wangb

a Institut für Mathematik, Universität Potsdam, 14476 Potsdam, Germany
b Department of Mathematics, Columbia University, New York NY 10027, USA
c Institut für Mathematik, Universität Augsburg, 86135 Augsburg, Germany
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DOI: https://doi.org/10.3842/SIGMA.2024.035
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.
Keywords: scalar curvature, warped product, bandwidth estimate, Llarull's theorem, holographic index theorem.
Funding agency Grant number
Deutsche Forschungsgemeinschaft
National Science Foundation DMS-2103573
Simons Foundation
Universidad Nacional de Colombia
The first named author was supported by DFG-SPP 2026 “Geometry at Infinity”. The second named author was supported by the National Science Foundation under grant DMS-2103573 and by the Simons Foundation. The third named author was supported by DFG-SPP 2026 “Geometry at Infinity” and by Columbia University.
Received: June 9, 2023; in final form April 8, 2024; Published online April 18, 2024
Document Type: Article
MSC: 53C20, 53C21, 53C27
Language: English
Citation: Christian Bär, Simon Brendle, Bernhard Hanke, Yipeng Wang, “Scalar Curvature Rigidity of Warped Product Metrics”, SIGMA, 20 (2024), 035, 26 pp.
Citation in format AMSBIB
\Bibitem{BarBreHan24}
\by Christian~B\"ar, Simon~Brendle, Bernhard~Hanke, Yipeng~Wang
\paper Scalar Curvature Rigidity of Warped Product Metrics
\jour SIGMA
\yr 2024
\vol 20
\papernumber 035
\totalpages 26
\mathnet{http://mi.mathnet.ru/sigma2037}
\crossref{https://doi.org/10.3842/SIGMA.2024.035}
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    		Symmetry, Integrability and Geometry: Methods and Applications
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