Variedades completas com espectro positivo

Abstract

In this dissertation we will present a theorem about the ends of complete manifold due to Peter Li and Jiaping Wang. This result can be interpreted as a generalization of Cheeger-Gromoll splitting theorem, which states that a complete Riemannian manifold M with nonnegative Ricci curvature then M has only one end or M is isometric to a product space R L, where L is a compact Riemannian manifold with nonnegative Ricci curvature. What Li-Wang did was expand this result for manifolds with Ricci curvature bounded from below by a nonnegative constant.