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arXiv · 2409.14503

Scalar-mean rigidity theorem for compact manifolds with boundary

Jinmin Wang·Zhichao Wang·Bo Zhu
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Abstract

We prove a scalar-mean rigidity theorem for compact Riemannian manifolds with boundary in dimension less than five by developing a dimension reduction argument for mean curvature, which extends Schoen-Yau's dimension reduction argument for scalar curvature. As a corollary, we prove the sharp spherical radius rigidity theorem and best NNSC fill-in in terms of the mean curvature. Moreover, we prove a Lipschitz Listing type scalar-mean rigidity theorem for these dimensions.

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Jinmin Wang, Zhichao Wang, Bo Zhu. 2025-03-05. Scalar-mean rigidity theorem for compact manifolds with boundary. https://arxiv.org/abs/2409.14503

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