Ricci flow in milnor frames oxford university research archive. The entropy formula for the ricci flow and its geometric applications. The ricci flow equation, introduced by richard hamilton h 1, is the evolution equation d dt gijt. Pdf recent developments on the hamiltons ricci flow. A major direction in ricci flow, via hamilton s and perelmans works, is the use of ricci flow as an approach to solving the poincare conjecture and thurstons geometrization conjecture. An introduction to hamiltons ricci flow olga iacovlenco department of mathematics and statistics, mcgill university, montreal, quebec, canada abstract in this project we study the ricci ow equation introduced by richard hamilton in 1982. Ricci flow is a means of processing the metric g by allowing it to evolve under.
Readership graduate students and research mathematicians interested in geometric analysis, the poincare conjecture, thurstons geometrization conjecture, and. The ricci ow is a pde for evolving the metric tensor in a riemannian manifold to make it \rounder, in. Hamilton himself and many other researchers like cao 16, yau 31, chow and others 5, perelman 14, 15, morgan and tian 19 developed the theory of ricci flow. In differential geometry, the ricci flow is an intrinsic geometric flow. Kahlerricci flow on complete manifolds ucsd mathematics. When the manifold is compact, perelman did talk about the results of bounding the scalar curvature and diameter for kahlerricci flow on compact manifolds with. For a general introduction to the subject of the ricci. Ricci flows of ricci flat cones research collection eth zurich. The ricci ow exhibits many similarities with the heat equation.
Pdf equivalence of simplicial ricci flow and hamiltons. The ricci flow is a pde for evolving the metric tensor in a riemannian manifold to make it rounder, in the hope that one may draw topological conclusions from. States, i have connected with many important figures in the topic of ricci flow and differential. The ricci flow, named after gregorio ricci curbastro, was first introduced by richard s. Abstract the aim of this project is to introduce the basics of hamilton s ricci flow. Since its introduction in 1904, the role of the ricci curvature has never stopped to.
Dimensional reduction and the longtime behavior of ricci flow. It is the primary tool used in grigori perelmans solution of the poincare conjecture, as well as in the proof of the differentiable sphere theorem by simon brendle and richard schoen. Hamilton in 1981 and is also referred to as the ricci hamilton flow. In this paper, we give a complete proof of the poincar. Indeed, hamilton believed that ricci flow could be used to establish the poincare conjecture and more general. Equivalence of simplicial ricci flow and hamilton s ricci flow for 3d neckpinch geometries. This work depends on the accumulative works of many geometric analysts in the past thirty years. Professor hyam rubinstein honours thesis, november 2006. Since the ricci flow is a nonlinear heat equation for the riemannian metric, the intuition is that it should smooth out the metric and thereby give rise, in the long. Given a complete riemannian manifold mn,gij, hamiltons ricci flow. A complete proof of the poincare and geometrization conjectures application of the hamiltonperelman theory of the ricci flow pdf.