Tohoku Mathematical Journal

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

Yohei Sakurai

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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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Tohoku Math. J. (2), Volume 71, Number 1 (2019), 69-109.

First available in Project Euclid: 9 March 2019

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Zentralblatt MATH identifier

Primary: 53C20: Global Riemannian geometry, including pinching [See also 31C12, 58B20]

manifold with boundary Bakry-Émery Ricci curvature


Sakurai, Yohei. Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound. Tohoku Math. J. (2) 71 (2019), no. 1, 69--109. doi:10.2748/tmj/1552100443.

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