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arXiv · 2306.06567

Multiplicity results for constant Q-curvature conformal metrics

Salomón Alarcón·Jimmy Petean·Carolina Rey
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Abstract

We prove that certain subcritical Paneitz-Branson type equations on a closed Riemannian manifold $(M,g)$ have at least $\mathrm{Cat}(M)$ positIve solutions, where $\mathrm{Cat}(M)$ is the Lusternik-Schnirelmann category of $M$. This implies that if $(X,h)$ is a closed positive Einstein manifold then for $\ep >0$ small enough there are at least $\mathrm{Cat}(M)$ metrics of constant $Q$-curvature in the conformal class of the Riemannian product $g+\ep h$.

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Salomón Alarcón, Jimmy Petean, Carolina Rey. 2023-06-11. Multiplicity results for constant Q-curvature conformal metrics. https://arxiv.org/abs/2306.06567

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