Given a compact four dimensional manifold, we prove existence of conformal metrics with constant Q-curvature under generic assumptions. The problem amounts to solving a fourth-order nonlinear elliptic equation with variational structure. Since the corresponding Euler functional is in general unbounded from above and from below, we employ topological methods and min-max schemes, jointly with the compactness result by Malchiodi.
|Titolo:||Existence of conformal metrics with constant $Q$-curvature|
|Data di pubblicazione:||2008|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.4007/annals.2008.168.813|
|Appare nelle tipologie:||1.1 Articolo in rivista|