Ancient solutions to the Ricci flow in dimension $3$

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2018-11-06 DOI:10.4310/acta.2020.v225.n1.a1

S. Brendle

引用次数: 60

Abstract

It is known from work of Perelman that any finite-time singularity of the Ricci flow on a compact three-manifold is modeled on an ancient $\kappa$-solution. We prove that the every noncompact ancient $\kappa$-solution in dimension $3$ is isometric to either the shrinking cylinders (or a quotient thereof), or the Bryant soliton.

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利玛窦流的古代解法（3美元）$

从Perelman的工作中可以知道，紧致三流形上Ricci流的任何有限时间奇异性都是在一个古老的$\kappa$-解上建模的。我们证明了维数$3$中的每一个非紧古$\kappa$-解与收缩圆柱体（或其商）或Bryant孤立子是等距的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

ACS Applied Energy Materials Materials Science-Materials Chemistry

CiteScore

10.30

自引率

6.20%

发文量

1368

期刊介绍： ACS Applied Energy Materials is an interdisciplinary journal publishing original research covering all aspects of materials, engineering, chemistry, physics and biology relevant to energy conversion and storage. The journal is devoted to reports of new and original experimental and theoretical research of an applied nature that integrate knowledge in the areas of materials, engineering, physics, bioscience, and chemistry into important energy applications.