TY - JOUR
T1 - The Yamabe flow on asymptotically flat manifolds
AU - Chen, Eric
AU - Wang, Yi
N1 - Publisher Copyright:
© 2023 Walter de Gruyter GmbH, Berlin/Boston.
PY - 2023/10
Y1 - 2023/10
N2 - We study the Yamabe flow starting from an asymptotically flat manifold (M n, g 0). We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if Y (M, [ g 0 ]) > 0, and show that the flow does not converge otherwise. If the scalar curvature is nonnegative and integrable, then the ADM mass at time infinity drops by the limit of the total scalar curvature along the flow.
AB - We study the Yamabe flow starting from an asymptotically flat manifold (M n, g 0). We show that the flow converges to an asymptotically flat, scalar flat metric in a weighted global sense if Y (M, [ g 0 ]) > 0, and show that the flow does not converge otherwise. If the scalar curvature is nonnegative and integrable, then the ADM mass at time infinity drops by the limit of the total scalar curvature along the flow.
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U2 - 10.1515/crelle-2023-0052
DO - 10.1515/crelle-2023-0052
M3 - Article
AN - SCOPUS:85170672158
SN - 0075-4102
VL - 2023
SP - 61
EP - 101
JO - Journal fur die Reine und Angewandte Mathematik
JF - Journal fur die Reine und Angewandte Mathematik
IS - 803
ER -