Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound

Abstract

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.

48 pages. arXiv admin note: text overlap with arXiv:1404.3845

References in corpus (1)

• Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound

Cited by in corpus (3)

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