Brunn-Minkowski inequality for the 1-Riesz capacity and level set convexity for the 1/2-Laplacian

2014/01/17 by Matteo Novaga, Novaga, Matteo, Berardo Ruffini +1 · 1 citation
Mathematics · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #math.AP

paper · pdf · doi:10.48550/arxiv.1401.4322

9 pages

arxiv created 2014/01/17 · arxiv updated 2014/01/20

Abstract

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

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