Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem

Jiangcheng You; Heng Zhang

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arXiv · 2606.15372

Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem

Jiangcheng You·Heng Zhang

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Abstract

We prove Gromov's Euclidean endpoint $C^0$ rigidity conjecture. Let $g$ be a smooth complete metric on $\R^3$ with non-negative scalar curvature. If $$ |g-g_{\Euc}|=o(r^{-1}),\qquad r=|x|\to\infty, $$ then $(\R^3,g)$ is isometric to Euclidean space.

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BibTeX RIS

Jiangcheng You, Heng Zhang. 2026-06-13. Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem. https://arxiv.org/abs/2606.15372

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