2019 | OriginalPaper | Buchkapitel
Boundary Regularity of Mass-Minimizing Integral Currents and a Question of Almgren
verfasst von : Camillo De Lellis, Guido De Philippis, Jonas Hirsch, Annalisa Massaccesi
Erschienen in: 2017 MATRIX Annals
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
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.