Flatness results for nonlocal minimal cones and subgraphs

Alberto Farina, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 Bernstein-type 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.

Original languageEnglish
Pages (from-to)1281-1301
Number of pages21
JournalAnnali della Scuola normale superiore di Pisa - Classe di scienze
Issue number4
Publication statusPublished - 2019


Dive into the research topics of 'Flatness results for nonlocal minimal cones and subgraphs'. Together they form a unique fingerprint.

Cite this