Tohoku Mathematical Journal

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

Yohei Sakurai

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Abstract

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.

Article information

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

Dates
First available in Project Euclid: 9 March 2019

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1552100443

Digital Object Identifier
doi:10.2748/tmj/1552100443

Mathematical Reviews number (MathSciNet)
MR3920791

Zentralblatt MATH identifier
07060327

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

Keywords
manifold with boundary Bakry-Émery Ricci curvature

Citation

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. https://projecteuclid.org/euclid.tmj/1552100443


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