Degree theory on oriented infinite-dimensional varieties and the Morse number of minimal surfaces spanning a curve in 𝑅ⁿ. I. 𝑛≥4

Tromba, A. J.

doi:10.1090/S0002-9947-1985-0787972-7

Degree theory on oriented infinite-dimensional varieties and the Morse number of minimal surfaces spanning a curve in $\textbf {R}^ n$. I. $n\geq 4$
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Abstract:

A degree theory applicable to Plateau’s problem is developed and the Morse equality for minimal surfaces spanning a contour in ${{\mathbf {R}}^n},n \geq 4$, is proved.

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