Ricci Flow and Three Dimensional Manifolds with Positive Curvature

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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.