Rigidity of positive mass theorem with fast metric decay

2026/07/19 by Jianchun Chu, Man-Chun Lee, Jingbo Wan
#math.DG

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Abstract

In this work, we consider metrics on Euclidean space with nonnegative scalar curvature and rapid decay at infinity. We show that, in dimensions four and higher, any such metric is necessarily flat if its decay rate exceeds that of the Schwarzschild metric. This complements recent works by Mazurowski-Yao and You-Zhang, thereby establishing Gromov's conjecture on the rigidity of the positive mass theorem under fast metric decay in all dimensions.

Citations

• The mass of an asymptotically flat manifold
• A new proof of the positive energy theorem
• On the proof of the positive mass conjecture in general relativity

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