小曲率集中的流形

IF 2.4 1区数学 Q1 MATHEMATICS Annals of Pde Pub Date : 2024-10-03 DOI:10.1007/s40818-024-00183-y

Pak-Yeung Chan, Shaochuang Huang, Man-Chun Lee

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引用次数: 0

摘要

在这项工作中，我们在曲率集中度较小的流形上构建了具有积分赫塞斯约束的类距离函数，并利用它在曲率可能无界的流形上构建了利玛窦流。作为一种应用，我们研究了这些流形的几何结构，而不假定其曲率是有界的。特别是，我们证明了具有利玛窦下界、非负标量曲率、有界熵、阿尔福斯正则和小曲率集中的流形在拓扑上是欧几里得的。

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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Manifolds with Small Curvature Concentration

In this work, we construct distance like functions with integral Hessian bound on manifolds with small curvature concentration and use it to construct Ricci flows on manifolds with possibly unbounded curvature. As an application, we study the geometric structure of those manifolds without bounded curvature assumption. In particular, we show that manifolds with Ricci lower bound, non-negative scalar curvature, bounded entropy, Ahlfors n-regular and small curvature concentration are topologically Euclidean.

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