Abstract
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.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 61-101 |
| Number of pages | 41 |
| Journal | Journal fur die Reine und Angewandte Mathematik |
| Volume | 2023 |
| Issue number | 803 |
| Early online date | Sep 6 2023 |
| DOIs | |
| State | Published - Oct 2023 |
| Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics
- Applied Mathematics