JournalsrmiVol. 37, No. 6pp. 2191–2228

The sharp quantitative isocapacitary inequality

  • Guido De Philippis

    New York University, USA

  • Michele Marini

    SISSA, Trieste, Italy

  • Ekaterina Mukoseeva

    SISSA, Trieste, Italy
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Abstract

We prove a sharp quantitative form of the classical isocapacitary inequality. Namely, we show that the difference between the capacity of a set and that of a ball with the same volume bounds the square of the Fraenkel asymmetry of the set. This provides a positive answer to a conjecture of Hall, Hayman, and Weitsman (J. Analyse Math. ’91).

Cite this article

Guido De Philippis, Michele Marini, Ekaterina Mukoseeva, The sharp quantitative isocapacitary inequality. Rev. Mat. Iberoam. 37 (2021), no. 6, pp. 2191–2228

DOI 10.4171/RMI/1259