Abstract
AbstractFor discrete weighted graphs there is sufficient literature about the Cheeger cut and the Cheeger problem, but for metric graphs there are few results about these problems. Our aim is to study the Cheeger cut and the Cheeger problem in metric graphs. For that, we use the concept of total variation and perimeter in metric graphs introduced in Mazón (Math Eng 5(1):1–38, 2023. https://doi.org/10.3934/mine.2023009), which takes into account the jumps at the vertices of the functions of bounded variation. Moreover, we study the eigenvalue problem for the minus 1-Laplacian operator in metric graphs, whereby we give a method to solve the optimal Cheeger cut problem.
Funder
Ministerio de Ciencia, Innovación y Universidades
Publisher
Springer Science and Business Media LLC
Subject
Mathematical Physics,Algebra and Number Theory,Analysis
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