On the Gromov–Hausdorff limits of compact surfaces with boundary

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-10-01 DOI:10.1007/s10455-024-09973-w

Tobias Dott

引用次数: 0

Abstract

In this work we investigate Gromov–Hausdorff limits of compact surfaces carrying length metrics. More precisely, we consider the case where all surfaces have the same Euler characteristic. We give a complete description of the limit spaces and study their topological properties. Our investigation builds on the results of a previous work which treats the case of closed surfaces.

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关于有边界的紧凑曲面的格罗莫夫-豪斯多夫极限

在这项工作中，我们研究了携带长度度量的紧凑曲面的格罗莫夫-豪斯多夫极限。更确切地说，我们考虑了所有表面具有相同欧拉特征的情况。我们给出了极限空间的完整描述，并研究了它们的拓扑特性。我们的研究建立在前人处理封闭曲面情况的成果之上。

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

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.