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 different, 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.
On the growth of nonlocal catenoids / M. Cozzi, E. Valdinoci. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - 31:1(2020 Apr 04), pp. 237-248. [10.4171/RLM/888]
On the growth of nonlocal catenoids
M. Cozzi
;E. Valdinoci
2020
Abstract
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 different, 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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