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Abstract: In this paper we prove that, given a compact four dimensional smoothRiemannian manifold M,g with smooth boundary there exists a metric conformalto g with constant T-curvature, zero Q-curvature and zero mean curvature undergeneric and conformally invariant assumptions. The problem amounts to solving afourth order nonlinear elliptic boundary value problem BVP with boundaryconditions given by a third-order pseudodifferential operator, and homogeneousNeumann one. It has a variational structure, but since the correspondingEuler-Lagrange functional is in general unbounded from below, we look forsaddle points. In order to do this, we use topological arguments and min-maxmethods combined with a compactness result for the corresponding BVP.



Author: Cheikh Birahim Ndiaye

Source: https://arxiv.org/







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