函数的持久同源性

IF 1.2 2区数学 Q1 MATHEMATICS

Communications in Contemporary Mathematics Pub Date : 2023-12-30 DOI:10.1142/s0219199723500554

Ulrich Bauer, Anibal M. Medina-Mardones, Maximilian Schmahl

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引用次数: 0

摘要

我们引入了一大类函数的拓扑条件，确保其相关子级集滤波的持久同调模块承认持久图，这尤其意味着它们满足广义莫尔斯不等式。我们将莫尔斯和汤普金斯给出的不稳定最小面定理的原始证明重铸在一个严谨的现代框架中，以此说明这些结果的适用性。

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Persistent homology for functionals

We introduce topological conditions on a broad class of functionals that ensure that the persistent homology modules of their associated sublevel set filtration admit persistence diagrams, which, in particular, implies that they satisfy generalized Morse inequalities. We illustrate the applicability of these results by recasting the original proof of the Unstable Minimal Surface Theorem given by Morse and Tompkins in a modern and rigorous framework.

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来源期刊

Communications in Contemporary Mathematics 数学-数学

CiteScore

2.90

自引率

6.20%

发文量

审稿时长

>12 weeks

期刊介绍： With traditional boundaries between various specialized fields of mathematics becoming less and less visible, Communications in Contemporary Mathematics (CCM) presents the forefront of research in the fields of: Algebra, Analysis, Applied Mathematics, Dynamical Systems, Geometry, Mathematical Physics, Number Theory, Partial Differential Equations and Topology, among others. It provides a forum to stimulate interactions between different areas. Both original research papers and expository articles will be published.