Mass under the Ricci flow

2005/10/04 by Xianzhe Dai, Li Ma, Dai, Xianzhe +1
Mathematics · Physics and Astronomy · #53Jxx #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0510083

openalex publication_date 2005/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the change of the ADM mass of an ALE space along the Ricci flow. Thus we first show that the ALE property is preserved under the Ricci flow. Then, we show that the mass is invariant under the flow in dimension three (similar results hold in higher dimension with more assumptions). A consequence of this result is the following. Let (M,g) be an ALE manifold of dimension n=3. If m(g)≠ 0, then the Ricci flow starting at g can not have Euclidean space as its (uniform) limit.

Citations

• On the proof of the positive mass conjecture in general relativity
• A new proof of the positive energy theorem

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