Almost splitting maps, transformation theorems and smooth fibration theorems

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-04 DOI:10.1016/j.aim.2024.109914

Hongzhi Huang , Xian-Tao Huang

引用次数: 0

Abstract

In this paper, we introduce a notion, called generalized Reifenberg condition, under which we prove a smooth fibration theorem for collapsed manifolds with Ricci curvature bounded below, which gives a unified proof of smooth fibration theorems in many previous works (including the ones proved by Fukaya and Yamaguchi respectively). A key tool in the proof of this fibration theorem is the transformation technique for almost splitting maps, which originates from Cheeger-Naber ([16]) and Cheeger-Jiang-Naber ([14]). More precisely, we show that a transformation theorem of Cheeger-Jiang-Naber (see Proposition 7.7 in [14]) holds for possibly collapsed manifolds. Some other applications of the transformation theorems are given in this paper.

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几乎分割映射、变换定理和光滑纤维定理

在本文中，我们引入了一个称为广义雷芬伯格条件的概念，在此条件下，我们证明了里奇曲率下界的坍缩流形的光滑傅里叶定理，它给出了以往许多著作（包括深谷和山口分别证明的著作）中光滑傅里叶定理的统一证明。证明这个纤度定理的一个关键工具是几乎分裂映射的变换技术，它源于 Cheeger-Naber （[16]）和 Cheeger-Jiang-Naber （[14]）。更确切地说，我们证明了 Cheeger-Jiang-Naber 的一个变换定理（见 [14] 中的命题 7.7）对于可能坍缩的流形是成立的。本文还给出了变换定理的其他一些应用。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.