Published Paper

Inserted: 1 jul 2022
Last Updated: 17 nov 2025

Journal: J. London Math. Soc. (2)
Volume: 119
Number: 1
Pages: e12840
Year: 2024
Doi: 10.1112/jlms.12840

There is a minor mistake in the proof of Theorem 3.6 in the published version: when estimating P(E_k(i)) from above, one needs to bound it with m(Om)(h_N(Om)+1) rather than with 2m(Om)h_N(Om) (as h_N(Om) might be zero). The following inequalities change accordingly. The preprint contains the amended statement.

19 mar 2025: Communication from the London Mathematical Society. The paper "The Cheeger problem in abstract measure spaces" published in Journal of the London Mathematical Society is among the top 10 most-cited papers published by the journal in 2023 (citation data from Clarivate Analytics. Top cited articles published between January 1, 2023 and December 31, 2023).

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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• cheeger_abstract_meas_spaces_pp.pdf