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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

classification math.DGmath.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 2 Pith papers

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

  1. A scalar-mean curvature comparison theorem for manifolds with iterated conical singularities

    math.DG 2025-06 conditional novelty 7.0 of 10

    For spin manifolds with iterated conical singularities, scalar-mean curvature comparison forces equality and rigidity, and nonnegative scalar curvature implies nonnegative ADM mass.

  2. Abstract cone operators and Lipschitz rigidity for scalar curvature on singular manifolds

    math.DG 2025-05 accept novelty 7.0 of 10

    Odd-dimensional Llarull rigidity holds for Lipschitz area non-increasing maps and for manifolds with cone-like singularities, proved via spherical suspension and abstract cone operators.

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