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Sharp bottom spectrum and scalar curvature rigidity
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Sharp bottom spectrum and scalar curvature rigidity
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We establish a sharp upper bound for the bottom spectrum of the Beltrami Laplacian on universal covers of closed Riemannian manifolds with a scalar curvature lower bound. Moreover, we prove a scalar curvature rigidity theorem when this bound is achieved. Additionally, we prove a net characterization of scalar curvature for general complete noncompact Riemannian manifolds.
Forward citations
Cited by 2 Pith papers
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$L^\infty$-metrics on tori and Schoen's conjecture
Under a non-surjectivity assumption on the fundamental group homomorphism from the singular set, an L^∞ metric on a torus with non-negative scalar curvature outside a Minkowski dimension ≤ n-3+(n-1)^{-1} singular set ...
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Scalar curvature, sharp bottom spectrum and geometric rigidity
Closed manifolds with Sc_g ≥ -n(n-1) and λ₁(̃M,̃g)=(n-1)²/4 are hyperbolic under topological assumptions from previous work.
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