A Survey of Hamilton’s Program for the Ricci Flow on 3-manifolds

This is a purely expository article on Riemannian Ricci flow with emphasis on dimension three. None of the results in this paper are due to the author. In view of Hamilton’s vast works, Yau’s influence on the field, and Perelman’s recent inspiring paper on Ricci flow, there may be more interest in the area. The author has only partial knowledge of this field but hopefully this paper will help nonspecialists and graduate students to follow some of the recent developments. Unfortunately, this paper does not include the very recent work of Perelman [P], which hopefully will be addressed at some later time. A previous expository article on Ricci flow was written by H.-D. Cao and the author [CaCh], we refer to the bibliography in there for some more references. In [H7], Hamilton included a survey and then proved a plethora of new results on Ricci flow with particular emphasis on singularity analysis.