O teorema de comparação do hessiano e aplicações sobre variedades completas com curvatura de Ricci nao-negativa

Abstract

n this dissertation, as the title implies, we present the Hessian Comparison Theorem and Laplacian-related applications of the distance function over complete manifolds with non-negative Ricci curvature. In Chapter II, the Hessian Comparison Theorem and the Lemma of the Index, which is used in the proof of the referred theorem. On the other hand, in chapter III, five propositions are demonstrated, the first of which is the Laplacian Comparison Theorem. The second is a consequence of the first and the third generalizes the second in the sense of distributions. Finally, the last two propositions deal with the comparison with volumes, ending with the following corollary of proposition 5: A complete and non-compact Riemannian manifold M, with Ri,c(M) > 0, has infinite volume.