Ricci Flow and Three Dimensional Manifolds with Positive Curvature

More about the book

The book delves into the Ricci flow on differentiable manifolds, highlighting its significant advancements in understanding manifolds across various dimensions. It focuses particularly on low-dimensional manifolds, which have contributed to resolving the Poincaré conjecture. Key concepts include both normalized and unnormalized flows, along with an in-depth examination of the curvature tensor in three dimensions and its evolution. The importance of maximum principles in this context is also emphasized, showcasing their critical role in the study.