Constant Q-curvature metrics in arbitrary dimension |
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Authors: | Cheikh Birahim Ndiaye |
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Affiliation: | SISSA, via Beirut 2-4, 34014 Trieste, Italy |
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Abstract: | Working in a given conformal class, we prove existence of constant Q-curvature metrics on compact manifolds of arbitrary dimension under generic assumptions. The problem is equivalent to solving a nth-order non-linear elliptic differential (or integral) equation with variational structure, where n is the dimension of the manifold. Since the corresponding Euler functional is in general unbounded from above and below, we use critical point theory, jointly with a compactness result for the above equation. |
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Keywords: | Geometric PDEs Conformally invariant integral equations Pseudodifferential operators Blow-up analysis Variational methods Min-max schemes |
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