Fluxo de Ricci: existência, estimativas de curvatura, compacidade de Hamilton e aplicação

Abstract

In this work we study the Ricci ow given by Hamilton addressing existence and uniqueness, thus obtaining a solution defined in a time interval, then give some estimates of Bernstein-Bando-Shi,which will be shown that the norm of the Riemann curvature explodes a finite time. Then we study the notion of convergence given by Cheeger and Gromov of pointed Riemannian manifolds for state the compactness theorem of Hamilton thus giving a demonstration of the Poincaré conjecture in the case where the Ricci tensor is positive.