RIGIDITY OF MANIFOLDS WITH BOUNDARY UNDER A LOWER BAKRY-EMERY RICCI CURVATURE BOUND

摘要

We study Riemannian manifolds with boundary under a lower Bakry-Emery 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 theorems for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.