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Existence of isoperimetric regions in \({\mathbb{R}^{n}}\) with density

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Abstract

We prove the existence of isoperimetric regions in \({\mathbb{R}^{n}}\) with density under various hypotheses on the growth of the density. Along the way, we prove results on the boundedness of isoperimetric regions.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Williams College, Williamstown, 01267, MA, USA

    Frank Morgan

  2. Dipartimento di Matematica, Università di Pavia “F. Casorati”, via Ferrata 1, Pavia, 27100, Italy

    Aldo Pratelli

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  1. Frank Morgan
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  2. Aldo Pratelli
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Correspondence to Aldo Pratelli.

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Morgan, F., Pratelli, A. Existence of isoperimetric regions in \({\mathbb{R}^{n}}\) with density. Ann Glob Anal Geom 43, 331–365 (2013). https://doi.org/10.1007/s10455-012-9348-7

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  • DOI: https://doi.org/10.1007/s10455-012-9348-7

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