Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound

摘要

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