Ricci Flow and Three Dimensional Manifolds with Positive Curvature

The study of the Ricci flow on differentiable manifolds in general has led to great progress in the study of manifolds of any dimension. In particular manifolds of low dimension can be looked at in great depth and these ideas have recently led to a resolution of the Poincare conjecture. The concept of the normailized and is introduced as well as the unnormalized flow. The curvature tensor in dimension three is studied as well as the evolution of the curvature. It is seen that maximum principles play a vital role in this work.