Caffarelli, Roquejoffre and Savin (2010) introduced a notion of fractional minimal surface, which is a boundary of a set that is minimal with respect to an s-perimeter functional (0<s<1). Starting from the property that as s tends 1, the normalized s-permiter approaches the classical perimiter, we construct examples of complete fractional minimal surfaces for s close to 1.

This is joint work with Manuel del Pino (Universidad de Chile) and Juncheng Wei (Chinese University Of Hong Kong and University of British Columbia).