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Paperback. Zustand: New. In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. 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. This text originated from graduate courses given at ETH Zurich and Stanford University, and it is directed at graduate students and researchers. The reader is assumed to be familiar with basic Riemannian geometry, but no previous knowledge of Ricci flow is required.

Paperback. Zustand: Brand New. 176 pages. 10.00x7.00x0.38 inches. In Stock.

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Paperback. Zustand: New. In 1982, R. Hamilton introduced a nonlinear evolution equation for Riemannian metrics with the aim of finding canonical metrics on manifolds. This evolution equation is known as the Ricci flow, and it has since been used widely and with great success, most notably in Perelman's solution of the Poincare conjecture. Furthermore, various convergence theorems have been established. 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. This text originated from graduate courses given at ETH Zurich and Stanford University, and it is directed at graduate students and researchers. The reader is assumed to be familiar with basic Riemannian geometry, but no previous knowledge of Ricci flow is required.

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Hardcover. Zustand: Very Good. Hardcover (printed boards, no jacket) in very good condition. Clean and sound pages. Graduate Studies in Mathematics, volume 111. CM. Used.

paperback. Zustand: New. Paperback. Pub Date :2014-02-01 Pages: 211 Language: Chinese Publisher: Higher Education Press Ricci flow theory is one of the hot differential Ho. Use Ricci flow. Hamiiton prove any compact with positive Ricci curvature of three-dimensional manifolds diffeomorphic to a certain space ball forms. Since then. Ricci flow has been used to solve public problems in Riemannian geometry and three-dimensional topology prolonged unresolved. The main research: Mathematics translate books Ricci flow with.