Yamabe flow and ADM Mass on asymptotically flat manifolds

Details Yamabe flow and ADM Mass on asymptotically flat manifolds Yamabe flow and ADM Mass on asymptotically flat manifolds

2011-09-12

arxiv.org/abs/1109.2443v2

Mathematics

Differential Geometry

Scientific paper

In this paper, we investigate the behavior of ADM mass and Einstein-Hilbert functional under the Yamabe flow. Through studying the Yamabe flow by weighted spaces, we show that ADM mass and Einstein-Hilbert functional are well-defined and monotone non-increasing under the Yamabe flow on $n$-dimensional, $n\geq 3$, asymptotically flat manifolds. In the case of dimension $n=3$ or 4, we obtain that the ADM mass is invariant under the Yamabe flow and the Yamabe flow is the gradient flow of Einstein-Hilbert functional on asymptotically flat manifolds

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