Topological methods for the resonant [formula omitted]-curvature problem in arbitrary even dimension

Abstract

This paper is devoted to the problem of existence of conformal metrics with prescribed Q-curvature on closed Riemannian manifolds of even dimension n≥4, when the kernel of the associated GJMS operator is trivial and the total integral of the corresponding Q-curvature is a positive integer multiple of the one of the n-dimensional round sphere. Indeed, exploiting the variational structure of the problem, we develop a full Morse theory and algebraic topological arguments for existence for this non-compact geometric variational problem of high order, extending the works Ahmedou and Ndiaye (2019) and Ndiaye (2015) to arbitrary even dimensions.