Bounds for capacities in terms of asymmetry

  • Tilak Bhattacharya, Allen Weitsman


The inequality (1.3) was conjectured by L. E. Fraenkel and, as noted in [6], the exponent 2 in (1.3) is sharp. The proof in [7] relies on an inequality between capacity and moment of inertia which had been proved by Pólya and Szegö [10 ; p 126] for connected sets. For general sets, this inequality had remained open until Hansen and Nadirashvili’s ingenious… (More)

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