Geodesic distance on Sierpinski-like carpet

IF 1.2 3区数学 Q1 MATHEMATICS

Journal of Mathematical Analysis and Applications Pub Date : 2025-04-03 DOI:10.1016/j.jmaa.2025.129541

Ying Lu , Qingcheng Zeng , Jiajun Xu , Lifeng Xi

引用次数: 0

Abstract

On the Sierpinski-like carpet, we study some conditions to ensure any two points can be connected by a rectifiable path on the carpet and the geodesic distance is comparable to the Manhattan distance. Based on these results, we obtain the Hausdorff dimension of skeleton network of Sierpinski-like carpet.

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席尔宾斯基式地毯上的测地线距离

在类似sierpinski的地毯上，我们研究了一些条件，以确保任何两点可以通过地毯上的可整流路径连接，并且测地线距离与曼哈顿距离相当。基于这些结果，我们得到了类sierpinski地毯骨架网络的Hausdorff维数。

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

Journal of Mathematical Analysis and Applications 数学-数学

CiteScore

2.50

自引率

7.70%

发文量

790

审稿时长

6 months

期刊介绍： The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.