Published Paper

Inserted: 1 jul 2022
Last Updated: 26 dec 2023

Journal: J. London Math. Soc.
Volume: 119
Number: 1
Pages: e12840
Year: 2024
Doi: 10.1112/jlms.12840

Abstract:

We consider non-negative $\sigma$-finite measure spaces coupled with a proper functional $P$ that plays the role of a perimeter. We introduce the Cheeger problem in this framework and extend many classical results on the Cheeger constant and on Cheeger sets to this setting, requiring minimal assumptions on the pair measure space-perimeter. Throughout the paper, the measure space will never be asked to be metric, at most topological, and this requires the introduction of a suitable notion of Sobolev spaces, induced by the coarea formula with the given perimeter.

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