Sufficient conditions for a pair of n-planes to be area-minimizing
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.
scientific article; zbMATH DE number 4084444