Uniqueness and stability of Ricci flow through singularities

IF 5.4 3区材料科学 Q2 CHEMISTRY, PHYSICAL

ACS Applied Energy Materials Pub Date : 2017-09-13 DOI:10.4310/acta.2022.v228.n1.a1

R. Bamler, B. Kleiner

引用次数: 30

Abstract

We verify a conjecture of Perelman, which states that there exists a canonical Ricci flow through singularities starting from an arbitrary compact Riemannian 3-manifold. Our main result is a uniqueness theorem for such flows, which, together with an earlier existence theorem of Lott and the second named author, implies Perelman's conjecture. We also show that this flow through singularities depends continuously on its initial condition and that it may be obtained as a limit of Ricci flows with surgery. Our results have applications to the study of diffeomorphism groups of three manifolds --- in particular to the Generalized Smale Conjecture --- which will appear in a subsequent paper.

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Ricci流通过奇点的唯一性和稳定性

我们验证了Perelman的一个猜想，该猜想指出从任意紧致黎曼3-流形出发，存在经过奇点的正则Ricci流。我们的主要结果是这类流的唯一性定理，它与Lott和第二位作者的一个较早的存在性定理一起，蕴涵了Perelman猜想。我们还证明了这种通过奇点的流动连续地依赖于它的初始条件，并且它可以作为里奇流的一个极限而得到。我们的结果可以应用于三流形的微分同态群的研究——特别是广义小猜想——这将在后续的论文中出现。

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.