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arXiv · 2605.29915

Rigidity in the Positive Mass Theorem with $C^0$ Decay

Liam Mazurowski·Xuan Yao
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Abstract

Let $g$ be a smooth metric on $\mathbb R^3$ with non-negative scalar curvature. We show that if $g$ satisfies $\vert g(x)-g_{\text{euc}}(x)\vert = O(\vert x\vert^{-1-\tau})$ for some $\tau > 0$ then $g$ must be flat.

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Liam Mazurowski, Xuan Yao. 2026-05-28. Rigidity in the Positive Mass Theorem with $C^0$ Decay. https://arxiv.org/abs/2605.29915

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