Size-minimizing rectifiable currents
type: Item
instance of: scholarly article
title: Size-minimizing rectifiable currents
zbMATH Open document ID: 0645.49024
DOI: 10.1007/BF01393966
author: Frank Morgan
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143681
review text: Traditionally in computing the area of a surface (rectifiable current) one counts multiplicities. Size is an alternative to area which does not count multiplicities. This paper gives some of the first existence results for size-minimizing rectifiable currents, for hypersurfaces with given external boundary. It presents what geometric measure theory can say about regularity, isoperimetric inequalities, and size bounds. Finally, it proves a generalization of Bernstein's theorem: a complete 2- dimensional size-minimizing surface S in \({\mathbb{R}}^ 3 \)is a plane, three half-planes meeting along a line at 120\(\circ\) angles, or the cone over the 1-skeleton of the regular tetrahedron.
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 53A10
zbMATH DE Number: 4052428
zbMATH Keywords: rectifiable current
zbMATH Keywords: size-minimizing
zbMATH Keywords: hypersurfaces with given external boundary
zbMATH Keywords: Bernstein's theorem
MaRDI profile type: Publication
Wikidata QID: Q125687498
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description: scientific article; zbMATH DE number 4052428