RIGIDITY OF MANIFOLDS WITH BOUNDARY UNDER A LOWER BAKRY-ÉMERY RICCI CURVATURE BOUND
2019 年 71 巻 1 号 p. 69-109
詳細
2019 年 71 巻 1 号 p. 69-109
We study Riemannian manifolds with boundary under a lower Bakry-Émery 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.
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