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京东 11.11 红包
Ben Andrews:Ricci flow on the two-sphere——1
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https://www.youtube.com/watch?v=pBCB_GohB50 Australian Geometric PDE Seminar Homepage:https://oz-geom-pde.github.io/season02/ Season 02 - 3d Ricci Flow Ben Andrews (ANU) 29 April 2022 Ben Andrews discusses the Hamilton/Chow proof that Ricci flow on the two-surface converges to the constant curvature metric. The proof makes use of the Harnack inequality and an entropy estimate. Ben Andrews , Christopher Hopper——“The Ricci Flow in Riemannian Geometry——A Complete Proof of the Differentiable 1/4-Pinching Sphere Theorem”:https://doi.org/10.1007/978-3-642-16286-2 This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's noncollapsing results, and culminating in a detailed analysis of the evolution of curvature, where recent breakthroughs of Böhm and Wilking and Brendle and Schoen have led to a proof of the differentiable 1/4-pinching sphere theorem. Peter Topping——“Lectures on the Ricci Flow”:https://doi.org/10.1017/CBO9780511721465 Simon Brendle——“Ricci Flow and the Sphere Theorem”——AMS——Graduate Studies in Mathematics This book provides a concise introduction to the subject as well as a comprehensive account of the convergence theory for the Ricci flow. The proofs rely mostly on maximum principle arguments. Special emphasis is placed on preserved curvature conditions, such as positive isotropic curvature. One of the major consequences of this theory is the Differentiable Sphere Theorem: a compact Riemannian manifold, whose sectional curvatures all lie in the interval (1,4], is diffeomorphic to a spherical space form. This question has a long history, dating back to a seminal paper by H. E. Rauch in 1951, and it was resolved in 2007 by the author and Richard Schoen. John W. Morgan, Gang Tian——“Ricci Flow and the Poincare Conjecture”——AMS&Clay Mathematics Monographs
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