  We prove that in Euclidean space $R^{n+1}$ any compact immersed nonnegatively
curved hypersurface $M$ with free boundary on the sphere $S^n$ is an embedded
convex topological disk. In particular, when the $m^{th}$ mean curvature of $M$
is constant, for any $1\leq m\leq n$, $M$ is a spherical cap or an equatorial
disk.
