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arXiv · 2503.04025

Scalar curvature rigidity of domains in a 3-dimensional warped product

Xiaoxiang Chai·Gaoming Wang
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Abstract

A warped product with a spherical factor and a logarithmically concave warping function satisfies a scalar curvature rigidity of the Llarull type. We develop a scalar curvature rigidity of the Llarull type for a general class of domains in a three dimensional spherical warped product. In the presence of rotational symmetry, we identify this class of domains as those satisfying a boundary condition analogous to the logarithmic concavity of the warping function.

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Xiaoxiang Chai, Gaoming Wang. 2025-03-06. Scalar curvature rigidity of domains in a 3-dimensional warped product. https://arxiv.org/abs/2503.04025

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