Flatness results for nonlocal minimal cones and subgraphs
2019
We show that nonlocal minimal cones which are non-singular subgraphs
outside the origin are necessarily halfspaces.
The proof is based on classical ideas of [14] and on the computation of the
linearized nonlocal mean curvature operator, which is proved to satisfy a suitable
maximum principle.
With this, we obtain new, and somehow simpler, proofs of the Bernsteintype
results for nonlocal minimal surfaces which have been recently established
in [20]. In addition, we establish a new nonlocal Bernstein-Moser-type result
which classifies Lipschitz nonlocal minimal subgraphs outside a ball.
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