Scalar curvature, sharp bottom spectrum and geometric rigidity

Jinmin Wang; Bo Zhu

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arXiv · 2606.11957

Scalar curvature, sharp bottom spectrum and geometric rigidity

Jinmin Wang·Bo Zhu

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Abstract

We prove rigidity in the equality case of the sharp bottom spectrum estimate under scalar curvature lower bound. Under the same topological assumptions as in our previous work, a closed manifold $(M,g)$ with $\mathrm{Sc}_g\geq -n(n-1)$ and $\lambda_1(\widetilde M,\widetilde g)=(n-1)^2/4$ must be hyperbolic. This gives rigidity results for closed hyperbolic manifolds and for closed manifolds admitting a metric of nonpositive sectional curvature.

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Jinmin Wang, Bo Zhu. 2026-06-10. Scalar curvature, sharp bottom spectrum and geometric rigidity. https://arxiv.org/abs/2606.11957

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