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Quantitative isoperimetric inequalities in \(\mathbb {H}^n\)

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Abstract

In the Heisenberg group \(\mathbb {H}^{n}\), \(n\ge 1\), we prove quantitative isoperimetric inequalities for Pansu’s spheres, that are known to be isoperimetric under various assumptions. The inequalities are shown for suitably restricted classes of competing sets and the proof relies on the construction of sub-calibrations.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Padova, via Trieste 63, 35121, Padua, Italy

    Valentina Franceschi & Roberto Monti

  2. Dipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio Emilia, via Campi 213/b, 41125, Modena, Italy

    Gian Paolo Leonardi

Authors
  1. Valentina Franceschi
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  2. Gian Paolo Leonardi
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  3. Roberto Monti
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Correspondence to Roberto Monti.

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Communicated by L. Ambrosio.

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Franceschi, V., Leonardi, G.P. & Monti, R. Quantitative isoperimetric inequalities in \(\mathbb {H}^n\) . Calc. Var. 54, 3229–3239 (2015). https://doi.org/10.1007/s00526-015-0899-x

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  • DOI: https://doi.org/10.1007/s00526-015-0899-x

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