Abstract
Part of our project consists in the study of general hypotheses on a certain class of surfaces in order to guarantee uniqueness of spheres immersed in three-dimensional Riemannian manifolds, in the sense of the generalized version of Hopf's Theorem proved by J.A. Gálvez and P. Mira (Uniqueness of immersed spheres in three-manifolds, to appear in Journal of Differential Geometry). We also …