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Llarull's theorem on punctured sphere with L^infty metric

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arxiv 2405.19724 v2 pith:WYHS64JK submitted 2024-05-30 math.DG math.MG

Llarull's theorem on punctured sphere with $L^\infty$ metric

classification math.DG math.MG
keywords metricllarulltheoreminftypuncturedspheresphericalstandard
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abstract

The classical Llarull theorem states that a smooth metric on $n$-sphere cannot have scalar curvature no less than $n(n-1)$ and dominate the standard spherical metric at the same time unless it is the standard spherical metric. In this work, we prove that Llarull's rigidity theorem holds for $L^{\infty}$ metrics on spheres with finitely many points punctured. This is related to a question of Gromov.

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Cited by 3 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. Lipschitz rigidity for scalar curvature on singular manifolds in odd dimensions

    math.DG 2026-04 unverdicted novelty 5.0

    A Llarull-type rigidity result for scalar curvature holds on odd-dimensional Riemannian spin manifolds with cone-like singularities via twisted Dirac operators and spectral flow.

  3. Scalar curvature rigidity of spheres with subsets removed and $L^\infty$ metrics

    math.DG 2024-07 unverdicted novelty 5.0

    Proves scalar curvature rigidity for L^∞ metrics on S^n minus high-codimension subsets with wrapping property, plus analogous result for tori and positive mass theorem corollary for L^∞ AF spin manifolds.