Resumen de On the non-uniqueness of conformal metrics with prescribed scalar and mean curvatures on compact manifolds with boundary

Gonzalo García Camacho, Jhovanny Muñoz

• For a compact Riemannian manifold (Mn,g) with boundary and dimension n, with n ≥ 2, we study the existence of metrics in the conformal class of g with scalar curvature Rg and mean curvature hg on the boundary. In this paper we find sufficient and necessary conditions for the existence of a smaller metric g' < g with curvatures Rg' = Rg and hg' = hg. Furthermore, we establish the uniqueness of such a metric g' in the conformal class of the metric g when Rg ≥ 0.