Foliation by bi-rotational self shrinkers in Euclidean space

Abstract

In this note, we prove that there exist two families of bi-rotational asymptotically conical self shrinkers with boundary called `trumpets', and two families of bi-rotational self shrinkers with boundary which close up called `disks', so that these families together with two generalized self shrinking cylinders, and a minimal cone foliate the whole space except some compact set containing the origin.