Published Paper

Inserted: 27 dec 2014
Last Updated: 19 aug 2024

Journal: J. Reine Angew. Math.
Year: 2017

Abstract:

We prove that, in every dimension, Lipschitz nonlocal minimal surfaces are smooth. Also, we extend to the nonlocal setting a famous theorem of De Giorgi stating that the validity of Bernstein’s theorem in dimension \( n + 1 \) is a consequence of the nonexistence of \( n \)-dimensional singular minimal cones in \( \mathbb{R}^n \).

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• lip_crelle_revised.pdf