Sufficient conditions for a pair of n-planes to be area-minimizing
type: Item
instance of: scholarly article
title: Sufficient conditions for a pair of n-planes to be area-minimizing
zbMATH Open document ID: 0663.49020
DOI: 10.1007/BF01456198
published in: Mathematische Annalen
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164314
review text: Let \(G_ 0(n,R^ m)\) be the Grassmannian of oriented n-planes in \(R^ m\) identified with the set of unit simple n-vectors in \(\Lambda_ nR^ m\). The author deals with the angle conjecture due to \textit{F. Morgan} [Trans. Am. Math. Soc. 276, 137-143 (1983; Zbl 0557.49022)]. ``Given \(\xi,\eta \in G_ 0(n,R^ m)\), with characterizing angles \(\theta_ 1,...,\theta_ n\), there exists a constant-coefficient differential form \(\phi \in \Lambda^ nR^ m\) such that \(<\xi,\phi >=1\), \(<\eta,\phi >=1\) if and only if \(\theta_ n\leq \theta_ 1+...+\theta_{n-1}''.\) An elegant and simple proof for the sufficiency in this conjecture is given and a preprint of G. Lawlor is mentioned which contains a proof for the necessity.
Mathematics Subject Classification ID: 49Q15
Mathematics Subject Classification ID: 15A75
zbMATH DE Number: 4084444
zbMATH Keywords: angle conjecture
zbMATH Keywords: sufficiency
author: Dana Mackenzie
reviewed by: Constantin Udrişte
MaRDI profile type: Publication
cites work: Calibrations on \(R^ 6\)
cites work: Q5565773
cites work: Calibrated geometries
cites work: The faces of the Grassmannian of 3-planes in \({\mathbb{R}}^ 7\) (calibrated geometries on \({\mathbb{R}}^ 7)\)
cites work: The angle criterion
cites work: The exterior algebra \(\Lambda ^ kR^ n\) and area minimization
cites work: On the Singular Structure of Three-Dimensional, Area-Minimizing Surfaces
OpenAlex ID: W2056318416
description: scientific article; zbMATH DE number 4084444