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The Brunn-Minkowski inequality for p-capacity of convex bodies

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Abstract.

In this paper we prove the Brunn-Minkowski inequality for the p-capacity of convex bodies (i.e convex compact sets with non-empty interior) in R n, for every p(1,n). Moreover we prove that the equality holds in such inequality if and only if the involved bodies coincide up to a translation and a dilatation.

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Authors and Affiliations

  1. Dipartimento di Matematica, ‘‘U. Dini’‘, Viale Morgagni 67/A, 50134, Firenze, Italy

    Andrea Colesanti & Paolo Salani

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  1. Andrea Colesanti
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  2. Paolo Salani
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Correspondence to Andrea Colesanti.

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Mathematics Subject Classification (2000): 35J60, 31B15, 39B62, 52A40

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Colesanti, A., Salani, P. The Brunn-Minkowski inequality for p-capacity of convex bodies. Math. Ann. 327, 459–479 (2003). https://doi.org/10.1007/s00208-003-0460-7

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  • DOI: https://doi.org/10.1007/s00208-003-0460-7

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