Minimal submanifolds with multiple isolated singularities

Abstract

We extend Smale's singular bridge principle [Ann. of Math. 130 (1989), 603-642] for $n$-dimensional strictly stable minimal cones in $\mathbb{R}^{n+1}$ $(n \geq 7$) to arbitrary codimension and each $n \geq 3$. We then apply the procedure to copies of the Lawson-Osserman cone to produce a four dimensional minimal graph in $\mathbb{R}^7$ with any finite number of isolated singularities.