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arxiv: 1303.0593 · v1 · pith:D5TM6F3Anew · submitted 2013-03-04 · 🧮 math.AP · math.DG

Nonlocal Minimal Lawson Cones

Juan Davila , Manuel del Pino , Juncheng Wei This is my paper
classification 🧮 math.AP math.DG
keywords minimalconesnonlocallawsonanalogcaffarellicaseclassical
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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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