TY - JOUR
T1 - On the growth of nonlocal catenoids
AU - Cozzi, Matteo
AU - Valdinoci, Enrico
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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.
AB - 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.
KW - Asymptotics
KW - Fractional perimeter
KW - Nonlocal catenoids
KW - Nonlocal minimal surfaces
UR - http://www.scopus.com/inward/record.url?scp=85086181716&partnerID=8YFLogxK
U2 - 10.4171/RLM/888
DO - 10.4171/RLM/888
M3 - Article
AN - SCOPUS:85086181716
SN - 1120-6330
VL - 31
SP - 237
EP - 248
JO - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
JF - Atti della Accademia Nazionale dei Lincei, Classe di Scienze Fisiche, Matematiche e Naturali, Rendiconti Lincei Matematica e Applicazioni
IS - 1
ER -