2019 | OriginalPaper | Chapter
Boundary Regularity of Mass-Minimizing Integral Currents and a Question of Almgren
Authors : Camillo De Lellis, Guido De Philippis, Jonas Hirsch, Annalisa Massaccesi
Published in: 2017 MATRIX Annals
Publisher: Springer International Publishing
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This short note is the announcement of a forthcoming work in which we prove a first general boundary regularity result for area-minimizing currents in higher codimension, without any geometric assumption on the boundary, except that it is an embedded submanifold of a Riemannian manifold, with a mild amount of smoothness ( C 3 , a 0 $$C^{3, a_0}$$ for a positive a 0 suffices). Our theorem allows to answer a question posed by Almgren at the end of his Big Regularity Paper. In this note we discuss the ideas of the proof and we also announce a theorem which shows that the boundary regularity is in general weaker that the interior regularity. Moreover we remark an interesting elementary byproduct on boundary monotonicity formulae.