度量对和度量元组的格罗莫夫-豪斯多夫收敛性

IF 0.6 4区数学 Q3 MATHEMATICS

Differential Geometry and its Applications Pub Date : 2024-04-02 DOI:10.1016/j.difgeo.2024.102135

Andrés Ahumada Gómez , Mauricio Che

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引用次数: 0

摘要

我们研究了度量对和度量元组的格罗莫夫-豪斯多夫收敛性，并证明了这一概念的不同自然定义的等价性。我们还证明了这种情况下的嵌入、完备性和紧凑性定理。最后，我们得到了 Fukaya 关于 Gromov-Hausdorff 等变收敛下商空间定理的一个相对版本，以及 Grove-Petersen-Wu 关于分层空间的有限性定理的一个版本。

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Gromov–Hausdorff convergence of metric pairs and metric tuples

We study the Gromov–Hausdorff convergence of metric pairs and metric tuples and prove the equivalence of different natural definitions of this concept. We also prove embedding, completeness and compactness theorems in this setting. Finally, we get a relative version of Fukaya's theorem about quotient spaces under Gromov–Hausdorff equivariant convergence and a version of Grove–Petersen–Wu's finiteness theorem for stratified spaces.

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来源期刊

Differential Geometry and its Applications 数学-数学

CiteScore

1.00

自引率

20.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential Geometry and its Applications publishes original research papers and survey papers in differential geometry and in all interdisciplinary areas in mathematics which use differential geometric methods and investigate geometrical structures. The following main areas are covered: differential equations on manifolds, global analysis, Lie groups, local and global differential geometry, the calculus of variations on manifolds, topology of manifolds, and mathematical physics.