## School of Mathematical and Statistical Sciences Faculty Publications and Presentations

#### Document Type

Book

#### Publication Date

2017

#### Abstract

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.

#### Recommended Citation

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/.

#### First Page

155

#### Last Page

192

#### Publication Title

Advances in Mathematics Research

## Comments

Published in Advances in Mathematics Research. ISBN: 978-1-53612-371-5