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

Yohei Sakurai

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arXiv · 1605.02493

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

Yohei Sakurai

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Abstract

We study Riemannian manifolds with boundary under a lower $N$-weighted Ricci curvature bound for $N$ at most $1$, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude 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.

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Yohei Sakurai. 2017-05-18. Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound. https://arxiv.org/abs/1605.02493

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