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

Authors: Liam Mazurowski, Xuan Yao

math.DG2026-05v1license

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.

Comments: 17 pages, comments are welcome!

Cite

@article{arxiv.2605.29915,
  title  = {Rigidity in the Positive Mass Theorem with $C^0$ Decay},
  author = {Liam Mazurowski and Xuan Yao},
  journal= {arXiv preprint arXiv:2605.29915},
  year   = {2026}
}

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