Ricci flow on asymptotically Euclidean manifolds

TL;DR

This paper proves that asymptotically Euclidean manifolds with nonnegative scalar curvature maintain nonnegative mass under Ricci flow and provides an independent proof of the positive mass theorem in three dimensions.

Contribution

It establishes the nonnegativity of mass under Ricci flow for asymptotically Euclidean manifolds with nonnegative scalar curvature and offers a new proof of the positive mass theorem in dimension three.

Findings

Mass remains nonnegative under Ricci flow for the specified manifolds.

Provides an independent proof of the positive mass theorem in 3D.

Confirms the stability of mass positivity in the Ricci flow evolution.

Abstract

In this paper, we prove that if an asymptotically Euclidean manifold $(M^n,g)$ under the condition that $R \ge 0$ has long time existence of Ricci flow, the mass of $(M^n,g)$ is nonnegative. In addition, we give an independent proof of positive mass theorem in dimension $3$.