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2019 Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound
Yohei Sakurai
Tohoku Math. J. (2) 71(1): 69-109 (2019). DOI: 10.2748/tmj/1552100443

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.

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Yohei Sakurai. "Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound." Tohoku Math. J. (2) 71 (1) 69 - 109, 2019. https://doi.org/10.2748/tmj/1552100443

Information

Published: 2019
First available in Project Euclid: 9 March 2019

zbMATH: 07060327
MathSciNet: MR3920791
Digital Object Identifier: 10.2748/tmj/1552100443

Subjects:
Primary: 53C20

Rights: Copyright © 2019 Tohoku University

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Vol.71 • No. 1 • 2019
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