The study of diferentiable manifolds is a deep an extensive area of mathematics. A technique such as the study of the Ricci flow turns out to be a very useful tool in this regard. This flow is an evolution of a Riemannian metric driven by a parabolic type of partial differential equation. It has attracted great interest recently due to its important achievements in geometry such as Perelman's proof of the geometrization conjecture and Brendle-Schoen's proof of the differentiable sphere theorem. It is the purpose here to give a comprehensive introduction to the Ricci flow on manifolds of dimension two which can be done in a reasonable fashion when the Euler characteristic is negative or zero. A brief introduction will be given to the case in which the Euler characteristic is positive.
Bracken, Paul. 2017. In Advances in Mathematics Research. Volume 22, edited by Albert R. Baswell. Vol. 22. Advances in Mathematics Research. Nova Science Publishers. https://novapublishers.com/shop/advances-in-mathematics-research-volume-22/.
Advances in Mathematics Research