On the topology and the boundary of N–dimensional RCD(K,N) spaces

IF 2 1区数学

Geometry & Topology Pub Date : 2019-07-04 DOI:10.2140/GT.2021.25.445

V. Kapovitch, A. Mondino

引用次数: 41

Abstract

We establish topological regularity and stability of N-dimensional RCD(K,N) spaces (up to a small singular set), also called non-collapsed RCD(K,N) in the literature. We also introduce the notion of a boundary of such spaces and study its properties, including its behavior under Gromov-Hausdorff convergence.

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关于N维RCD(K,N)空间的拓扑和边界

本文建立了N维RCD(K,N)空间(直到一个小奇异集)的拓扑正则性和稳定性，在文献中也称为非坍缩RCD(K,N)。我们还引入了这种空间的边界的概念，并研究了它的性质，包括它在Gromov-Hausdorff收敛下的行为。

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

Geometry & Topology 数学-数学

自引率

5.00%

发文量

期刊介绍： Geometry and Topology is a fully refereed journal covering all of geometry and topology, broadly understood. G&T is published in electronic and print formats by Mathematical Sciences Publishers. The purpose of Geometry & Topology is the advancement of mathematics. Editors evaluate submitted papers strictly on the basis of scientific merit, without regard to authors" nationality, country of residence, institutional affiliation, sex, ethnic origin, or political views.