Abstract
In this paper, we consider the total mass of asymptotically flat Riemannian manifold under the connection Ricci flow, which can also be viewed as renormalization group flow for nonlinear sigma model. Using the maximum principle, we show that the asymptotically Euclidean property is preserved under this flow. Moreover, if the decay rate of the AE manifold is fast enough, then the ADM mass is invariant under the flow.
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