Density of a minimal submanifold and total curvature of its boundary

Given a piecewise smooth submanifold Gamma(n-1) subset of R-m and p is an element of R-m, we define the vision angle Pi(p)(Gamma) to be the (n - 1)-dimensional volume of the radial projection of Gamma to the unit sphere centered at p. If p is a point on a stationary n-rectifiable set Sigma subset of R-m with boundary Gamma, then we show the density of Sigma at p is <= the density at its vertex p of the cone over Gamma. It follows that if Pi(p)(Gamma) is less than twice the volume of Sn-1, for all p is an element of Gamma, then S is an embedded submanifold. As a consequence, we prove that given two n-planes R-1(n), R-2(n) n R-m and two compact convex hypersurfaces Gamma(i) R-i(n), i=1, 2, a nonflat minimal submanifold spanned by Gamma := Gamma(1) boolean OR Gamma(2) isembedded.