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Journal of Convex Analysis 22 (2015), No. 4, 1125--1134
Copyright Heldermann Verlag 2015

Brunn-Minkowski Inequality for the 1-Riesz Capacity and Level Set Convexity for the 1/2-Laplacian

Matteo Novaga
Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

Berardo Ruffini
Institut Fourier, 100 Rue des Mathématiques, BP 74, 38402 St. Martin d'Hères, France

We prove that that the 1-Riesz capacity satisfies a Brunn-Minkowski inequality, and that the capacitary function of the 1/2-Laplacian is level set convex.

Keywords: Fractional Laplacian, Brunn-Minkowski inequality, level set convexity, Riesz capacity.

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