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Boundaries of prescribed mean curvature

Eduardo H. A. Gonzales;  Umberto Massari;  Italo Tamanini — 1993

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

The existence of a singular curve in R 2 is proven, whose curvature can be extended to an L 2 function. The curve is the boundary of a two dimensional set, minimizing the length plus the integral over the set of the extension of the curvature. The existence of such a curve was conjectured by E. De Giorgi, during a conference held in Trento in July 1992.

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