The sharp quantitative isocapacitary inequality

Guido de Philippis, Michele Marini, Ekaterina Mukoseeva

Research output: Contribution to journalArticlepeer-review


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).

Original languageEnglish (US)
Pages (from-to)2191-2228
Number of pages38
JournalRevista Matematica Iberoamericana
Issue number6
StatePublished - 2021


  • Fraenkel asymmetry
  • Isocapacitary inequality
  • Stability estimates

ASJC Scopus subject areas

  • General Mathematics


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