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arXiv:2407.10212 [math.DG]AbstractReferencesReviewsResources

Scalar curvature rigidity of domains in a warped product

Xiaoxiang Chai, Xueyuan Wan

Published 2024-07-14Version 1

By exploiting the conformality of a warped product metric with a direct product metric, we develop a new connection on a twisted spinor bundle and its associated Dirac operator. We obtain a Llarull type scalar curvature rigidity for a general class of domains in a warped product. Also, we are able to address Gromov dihedral rigidity in hyperbolic space assuming matching angles.

Comments: 32 pages, comments welcome. This preprint supersedes arXiv:2312.16022. A Llarull theorem is added in this paper, and we handle all dimensions; the rigidity of initial data sets would be in a separate paper
Categories: math.DG
Subjects: 53C24, 53C27, 53C21
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