Uniqueness of conformal metrics with prescribed scalar and mean curvatures on compact manifolds with boundary (2010)
Departamento de Matemáticas, Universidad del Valle, Calle 13 No. 100 - 00, Cali, ColombiaLet $(M^n, g)$ be a compact manifold with boundary and $n ≥ 2$. In this paper we prove the variational characterization of the Neumann eigen\-values of an elliptic operator associated to the problem of conformal deformation of metrics and we study the uniqueness of metrics in the conformal class of the metric $g$ having the same scalar curvature of the manifold and the same mean curvature of its boundary.