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

Jianchun Chu; Man-Chun Lee; Jintian Zhu

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arXiv · 2405.19724

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

Jianchun Chu·Man-Chun Lee·Jintian Zhu

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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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Jianchun Chu, Man-Chun Lee, Jintian Zhu. 2024-05-30. Llarull's theorem on punctured sphere with $L^\infty$ metric. https://arxiv.org/abs/2405.19724

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