On the singular structure of three-dimensional, area-minimizing surfaces

Morgan, Frank

doi:10.1090/S0002-9947-1983-0684498-4

On the singular structure of three-dimensional, area-minimizing surfaces
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Trans. Amer. Math. Soc. 276 (1983), 137-143 Request permission

Abstract:

A sufficient condition is given for the union of two three-dimensional planes through the origin in ${{\mathbf {R}}^n}$ to be area-minimizing. The condition is in terms of the three angles $0 \leqslant {\gamma _1} \leqslant {\gamma _2} \leqslant {\gamma _3}$ which characterize the geometric relationship between the planes. If ${\gamma _3} \leqslant {\gamma _1} + {\gamma _2}$, the union of the planes is area-minimizing.

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Multiple valued functions minimizing Dirichlet’s integral and the regularity of mass minimizing integral currents

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