  In this note we use the strong maximum principle and integral estimates prove
two results on minimal hypersurfaces $F:M^n\rightarrow\mathbb{R}^{n+1}$ with
free boundary on the standard unit sphere. First we show that if $F$ is
graphical with respect to any Killing field, then $F(M^n)$ is a flat disk. This
result is independent of the topology or number or boundaries. Second, if $M^n
= \mathbb{D}^n$ is a disk, we show the supremum of the curvature squared on the
interior is bounded below by $n$ times the infimum of the curvature squared on
the boundary. These may be combined the give an impression of the curvature of
non-flat minimal hyperdisks with free boundary.
