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Ricci flow on asymptotically Euclidean manifolds

2018; Mathematical Sciences Publishers; Volume: 22; Issue: 3 Linguagem: Inglês

10.2140/gt.2018.22.1837

1465-3060

Yu Li,

Point processes and geometric inequalities

Ricci flow on asymptotically Euclidean manifolds YU LIIn this paper, we prove that if an asymptotically Euclidean manifold with nonnegative scalar curvature has long-time existence of Ricci flow, the ADM mass is nonnegative.We also give an independent proof of the positive mass theorem in dimension three. 53C44; 83C99 Mass under Ricci flowWe prove in this section that Ricci flow preserves the AE condition and the mass is unchanged under Ricci flow.Our argument differs from that of Dai and Ma in [16] in that we fix an AE coordinate system along the flow.The main tool we use is the following maximum principle on the noncompact manifold with evolving metrics; see [11, Theorem 12.14].