Existence of conformal metrics with constant $Q$-curvature

Details Existence of conformal metrics with constant $Q$-curvature Existence of conformal metrics with constant $Q$-curvature

2004-10-06

arxiv.org/abs/math/0410141v3

Mathematics

Analysis of PDEs

36 pages, revised version. To appear in Annals of Mathematics

Scientific paper

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.

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