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arXiv · 1506.03223

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

Yohei Sakurai
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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.

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Yohei Sakurai. 2015-06-10. Rigidity of manifolds with boundary under a lower Bakry-E'mery Ricci curvature bound. https://arxiv.org/abs/1506.03223

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