The sharp quantitative isocapacitary inequality

Guido De Philippis ^[1] ; Michele Marini ^[2] ; Ekaterina Mukoseeva ^[2]
1. [1] New York University
  
  New York University
  
  Estados Unidos
2. [2] SISSA, Trieste
Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 37, Nº 6, 2021, págs. 2191-2228
Idioma: inglés
DOI: 10.4171/rmi/1259
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Resumen
- 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).