On the growth of nonlocal catenoids

  • Matteo Cozzi

    University of Bath, UK
  • Enrico Valdinoci

    University of Western Australia, Crawley, Australia
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As well known, classical catenoids in R3\mathbb 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.

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Matteo Cozzi, Enrico Valdinoci, On the growth of nonlocal catenoids. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 31 (2020), no. 1, pp. 237–248

DOI 10.4171/RLM/888