  In [AMW], it is proved that if a compact $3$-manifold has positive Ricci
curvature and strictly convex boundary, then this manifold is diffeomorphic to
the standard $3$-dimensional Euclidean disk. In this paper, we prove its
higher-dimensional generalization: if a compact $n$-manifold has positive
curvature operator and strictly convex boundary, then this manifold is
diffeomorphic to the standard $n$-dimensional Euclidean disk.
