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Existence of conformal metrics with constant $Q$-curvature

Zindine Djadli·Andrea Malchiodi
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Abstract

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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Zindine Djadli, Andrea Malchiodi. 2006-04-18. Existence of conformal metrics with constant $Q$-curvature. https://arxiv.org/abs/math/0410141

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