On the growth of nonlocal catenoids

Matteo Cozzi; Enrico Valdinoci

doi:10.4171/RLM/888

On the growth of nonlocal catenoids

Matteo Cozzi, Enrico Valdinoci

Department of Mathematical Sciences

The University of Western Australia

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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 language	English
Pages (from-to)	237-248
Number of pages	12
Journal	Rendiconti Lincei. Matematica e Applicazioni
Volume	31
Issue number	1
Early online date	3 Apr 2020
DOIs	https://doi.org/10.4171/RLM/888
Publication status	Published - 2020

Keywords

Asymptotics
Fractional perimeter
Nonlocal catenoids
Nonlocal minimal surfaces

ASJC Scopus subject areas

General Mathematics

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On the growth of nonlocal catenoids

Abstract

Keywords

ASJC Scopus subject areas

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