Concentration–compactness phenomena in the higher order Liouville's equation☆

By L. Martinazzi. 2008

60 citations recorded by the source corpus.

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 {R^2}, then that of a closed manifold and, finally, the particular case of the sphere {S^2m}. 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 {R^2m}, 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.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7ef09846b7d9a553d14c5a0f1a425fb1ba6923a4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Blow-up analysis of a nonlocal Liouville-type equation (2015, background): “(Also, higher-dimensional extensions were studied under the same strong assumptions of convergence of Kk in C0 or even C1; see, e.g., [Druet and Robert 2006; Malchiodi 2006; Martinazzi 2009b].)”
Supercritical conformal metrics on surfaces with conical singularities (2011, background): “5 (see also results in [4, 29]) where this hypothesis is required (see [38] for related issues in the regular case).”