Nonlocal Delaunay surfaces

Juan Dávila, Manuel del Pino, Serena Dipierro, Enrico Valdinoci

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We construct codimension surfaces of any dimension that minimize a periodic nonlocal perimeter functional among surfaces that are periodic, cylindrically symmetric and decreasing.

These surfaces may be seen as a nonlocal analogue of the classical Delaunay surfaces (onduloids). For small volume, most of their mass tends to be concentrated in a periodic array and the surfaces are close to a periodic array of balls (in fact, we give explicit quantitative bounds on these facts).
Original languageEnglish
Pages (from-to)357-380
Number of pages24
JournalNonlinear Analysis: Theory Methods & Applications
Early online date3 Nov 2015
Publication statusPublished - 1 May 2016


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