Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4591727 | Journal of Functional Analysis | 2009 | 29 Pages |
Abstract
We investigate different concentration–compactness and blow-up phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in R2m, then that of a closed manifold and, finally, the particular case of the sphere S2m. In all cases we allow the sign of the Q-curvature to vary, and show that in the case of a closed manifold, contrary to the case of open domains in R2m, blow-up phenomena can occur only at points of positive Q-curvature. As a consequence, on a locally conformally flat manifold of non-positive Euler characteristic we always have compactness.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory