Abstract
We prove that the regular \(N\)-gon minimizes the Cheeger constant among polygons with a given area and \(N\) sides.
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Acknowledgments
This work was supported by the ANR-12-BS01-0007 Optiform and GNAMPA (INDAM), and was finished during the first author’s visit at the Isaac Newton Institute for Mathematical Sciences, Cambridge, within the programme “Free Boundary Problems and Related Topics”.
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Communicated by Jiaping Wang.
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Bucur, D., Fragalà, I. A Faber–Krahn Inequality for the Cheeger Constant of \(N\)-gons. J Geom Anal 26, 88–117 (2016). https://doi.org/10.1007/s12220-014-9539-5
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DOI: https://doi.org/10.1007/s12220-014-9539-5