In a sequel to volume one and to volume two parts I, II, and III--on techniques and applications of Ricci flow--Chow and all focus on the long-term behavior of solutions to the Ricci flow, including the geometry of non-compact gradient Ricci solitons, ancient solutions, Hamiltonian's classification of three-dimensional non-singular solution, and the stability of the Ricci flow. Beginning with chapter 27, they consider such topics as special ancient solutions, compact two-dimensional ancient solutions, hyperbolic geometry and three-manifolds, constant mean curvature surfaces and harmonic maps by the implicit function theorem, and type II singularities and degenerate neckpinches. Annotation ©2015 Ringgold, Inc., Portland, OR (protoview.com)
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