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Sharp bottom spectrum and scalar curvature rigidity

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arxiv 2408.08245 v4 pith:5IJ57EJX submitted 2024-08-15 math.DG math.OA

Sharp bottom spectrum and scalar curvature rigidity

classification math.DG math.OA
keywords curvaturescalarboundbottommanifoldsproveriemannianrigidity
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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.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. $L^\infty$-metrics on tori and Schoen's conjecture

    math.DG 2026-06 unverdicted novelty 5.0

    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 ...

  2. Scalar curvature, sharp bottom spectrum and geometric rigidity

    math.DG 2026-06 unverdicted novelty 5.0

    Closed manifolds with Sc_g ≥ -n(n-1) and λ₁(̃M,̃g)=(n-1)²/4 are hyperbolic under topological assumptions from previous work.