Multiplicity results for constant Q-curvature conformal metrics

Author:

Salomón Alarcón, Jimmy Petean, Carolina Rey

Keyword:

Mathematics, Differential Geometry, Differential Geometry (math.DG), Analysis of PDEs (math.AP)

journal:

--

date:

2023-06-10 16:00:00

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 $g+\ep h$.