Proves that the harmonic mass of a continuous asymptotically flat metric on R^3 is non-negative, with equality only when the metric is flat.
Quantification of scalar curvature under $C^0$ convergence using smoothing
4 Pith papers cite this work. Polarity classification is still indexing.
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abstract
A quantitative version of the scalar lower bound under $C^0$ convergence was conjectured by Gromov. More recently, Mazurowski and Yao proved that a refined form of Gromov's conjecture holds in dimension three. Furthermore, they constructed examples demonstrating that such a refinement is necessary. In this paper, we establish that the refined quantitative bound holds in all dimensions greater than or equal to three.
fields
math.DG 4years
2026 4verdicts
UNVERDICTED 4representative citing papers
Proves that a smooth complete metric g on R^3 with Scal(g) >= 0 and |g - g_Euc| = o(r^{-1}) as r -> infinity is isometric to Euclidean space.
Defines scalar curvature lower bounds for C^0 3-metrics via IMCF Hawking mass monotonicity and states a stability theorem for nonnegative scalar curvature in this sense.
Smooth metrics on R^3 with non-negative scalar curvature and |g - g_euc| = O(|x|^{-1-τ}) for τ>0 are necessarily flat.
citing papers explorer
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A Positive Mass Theorem for Continuous Metrics
Proves that the harmonic mass of a continuous asymptotically flat metric on R^3 is non-negative, with equality only when the metric is flat.
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Gromov's Euclidean Endpoint $C^0$ Rigidity for the Positive Mass Theorem
Proves that a smooth complete metric g on R^3 with Scal(g) >= 0 and |g - g_Euc| = o(r^{-1}) as r -> infinity is isometric to Euclidean space.
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Scalar curvature bounds for 3D continuous metrics through the Inverse Mean Curvature Flow
Defines scalar curvature lower bounds for C^0 3-metrics via IMCF Hawking mass monotonicity and states a stability theorem for nonnegative scalar curvature in this sense.
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Rigidity in the Positive Mass Theorem with $C^0$ Decay
Smooth metrics on R^3 with non-negative scalar curvature and |g - g_euc| = O(|x|^{-1-τ}) for τ>0 are necessarily flat.