Nonlocal Minimal Lawson Cones

Published 4 Mar 2013 in math.AP and math.DG | (1303.0593v1)

Abstract: We prove the existence of the analog of Lawson's minimal cones for a notion of nonlocal minimal surface introduced by Caffarelli, Roquejoffre and Savin, and establish their stability/instability in low dimensions. In particular we find that there are nonlocal stable minimal cones in dimension 7, in contrast with the case of classical minimal surfaces.

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