Surgery for extended Ricci flow systems

Abstract

In this thesis extended Ricci flow systems, which are obtained by coupling Ricci flow to the harmonic map heat flow, are studied. The interest in this system stems from its connection to static solutions to the vacuum Einstein equations and Ricci flow on manifolds with warped product metrics. We prove a convergence theorem and a singularity classification theorem and construct the flow with surgery in the spirit of Hamilton and Perelman for three-dimensional solutions.