The Non Parametric Area Functional
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The study of minimal surfaces is central not only in the Calculus of Variations, but in several areas of mathematics. It has a long and rich history, and in particular by now we have a fairly complete understanding of graphs of real-valued functions of minimal area. In contrast, not much is known about graphs of minimal area in codimension larger than one. In this chapter we would like to illustrate some aspects of such a problem and discuss it in the setting of Cartesian currents.
KeywordsMinimal Surface Dirichlet Problem Parametric Area Rectifiable Current Plateau Problem
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