WIAS Preprint No. 2075, (2015)

Nonlocal Delaunay surfaces


  • Davila, Juan
  • del Pino, Manuel
  • Dipierro, Serena
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R11 49Q05 49Q20


  • Delaunay surfaces, nonlocal perimeter, minimization problem




We construct codimension 1 surfaces of any dimension that minimize a 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).

Appeared in

  • Nonlinear Anal., 137 (2016) pp. 357--380.

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