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Scalar curvature rigidity of domains in a warped product
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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.
Forward citations
Cited by 2 Pith papers
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Gap phenomenon for scalar curvature
Scalar curvature on any closed even-dimensional manifold with nonzero Euler characteristic can be increased by at most an explicit constant, the gap, which is a function of the minimal eigenvalue of the curvature oper...
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Scalar curvature rigidity of parabolically convex domains in hyperbolic spaces
A nonzero-degree map into a parabolically convex hyperbolic domain, with scalar curvature and boundary curvature bounds, forces the domain to be hyperbolic and the boundary map to be an isometry.
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