عنوان

Ricci flow and the sphere theorem /

شابک

0821849387

شابک

9780821849385

شماره

dltt

عنوان اصلي

Ricci flow and the sphere theorem /

نام عام مواد

[Book]

نام نخستين پديدآور

Simon Brendle

نام خاص و کميت اثر

vii, 176 pages ;

ابعاد

27 cm

عنوان فروست

Graduate studies in mathematics ;

مشخصه جلد

v. 111

متن يادداشت

Includes bibliographical references (pages [169]-173) and index

متن يادداشت

A survey of sphere theorems in geometry -- Hamilton's Ricci flow -- Interior estimates -- Ricci flow on S2 -- Pointwise curvature estimates -- Curvature pinching in dimension 3 -- Preserved curvature conditions in higher dimensions -- Convergence results in higher dimensions -- Rigidity results

بدون عنوان

0

متن يادداشت

"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."--Publisher's description

موضوع مستند نشده

Ricci flow

موضوع مستند نشده

Sphere

شماره

ويراست

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

Brendle, Simon,1981-

تاريخ عمليات

20100224122155.0

قواعد فهرست نويسي ( بخش توصيفي )

rda

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y