For a sequence of blow up solutions of the Yamabe equation on non-locally conformally flat compact Riemannian manifolds of dimension 10 or 11, we establish sharp estimates on its asymptotic profile near blow up points as well as sharp decay estimates of the Weyl tensor and its covariant derivatives at blow up points. If the Positive Mass Theorem held in dimensions 10 and 11, these estimates would imply the compactness of the set of solutions of the Yamabe equation on such manifolds.
|Original language||English (US)|
|Number of pages||37|
|Journal||Journal of Functional Analysis|
|State||Published - Apr 15 2007|
All Science Journal Classification (ASJC) codes
- Compactness of solutions
- Yamabe problem