On the growth of nonlocal catenoids

Matteo Cozzi, Enrico Valdinoci

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Abstract

As well known, classical catenoids in R 3 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
JournalRendiconti Lincei. Matematica e Applicazioni
Volume31
Issue number1
Early online date3 Apr 2020
DOIs
Publication statusPublished - 2020

Keywords

  • Asymptotics
  • Fractional perimeter
  • Nonlocal catenoids
  • Nonlocal minimal surfaces

ASJC Scopus subject areas

  • Mathematics(all)

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