On the first stability eigenvalue of constant mean curvature surfaces into homogeneous 3-manifolds

摘要

We find out upper bounds for the first eigenvalue of the stability operatorfor compact constant mean curvature surfaces immersed into certain3-dimensional Riemannian spaces, in particular into homogeneous 3-manifolds. Asan application we derive some consequences for strongly stable surfaces in suchambient spaces. Moreover, we also get a characterization of Hopf tori incertain Berger spheres.