Existence of conformal metrics with constant $Q$-curvature
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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 minimax schemes, jointly with a compactness result by the second author.
36 pages, revised version. To appear in Annals of Mathematics
36 pages, revised version. To appear in Annals of Mathematics