Year: 2026
Type: preprint
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. Our method also extend naturally to weakly asymptotically flat manifolds.
Source: arXiv (Cornell University)
Authors: Chu, Jianchun, Lee, Man-Chun, Wan, Jingbo
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7169873809