Scalar Curvature Rigidity of Warped Product Metrics

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2024
• ISSN: 1815-0659
• Main Authors: Bär, Christian, Brendle, Simon, Hanke, Bernhard, Wang, Yipeng
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2024
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/212160
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Scalar Curvature Rigidity of Warped Product Metrics. Christian Bär, Simon Brendle, Bernhard Hanke and Yipeng Wang. SIGMA 20 (2024), 035, 26 pages

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...