On the growth of nonlocal catenoids

Matteo Cozzi, Enrico Valdinoci

Research output: Contribution to journalArticlepeer-review


As well known, classical catenoids in R3 possess logarithmic growth at infinity. In this note we prove that the case of nonlocal minimal surfaces is significantly di¤erent, and indeed all nonlocal catenoids must grow at least linearly. More generally, we prove that stationary sets for the nonlocal perimeter functional which grow sublinearly at infinity are necessarily half-spaces.

Original languageEnglish
Pages (from-to)237-248
Number of pages12
JournalAtti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
Issue number1
Publication statusPublished - 1 Jan 2020


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