Density of a minimal submanifold and total curvature of its boundary

Jaigyoung Choe, Robert Gulliver

Given a piecewise smooth submanifold ${\Gamma }^{n-1}\subset {\mathbb{R}}^m$ and $p\in {\mathbb{R}}^m$, we define the {\em vision angle} ${\Pi }_p(\Gamma )$ to be the $(n-1)$-dimensional volume of the radial projectio…