  We study Riemannian manifolds with boundary under a lower Bakry-E'mery Ricci
curvature bound. In our weighted setting, we prove several rigidity theorems
for such manifolds with boundary. We conclude a rigidity theorem for the
inscribed radii, a volume growth rigidity theorem for the metric neighborhoods
of the boundaries, and various splitting theorems. We also obtain rigidity
results for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.
