Tohoku Mathematical Journal
2019
March
SECOND SERIES VOL. 71, NO. 1

Tohoku Math. J.
71 (2019), 69-109

Title RIGIDITY OF MANIFOLDS WITH BOUNDARY UNDER A LOWER BAKRY-\'EMERY RICCI CURVATURE BOUND

Author Yohei Sakurai

(Received December 25, 2015, revised September 14, 2016)
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.

Mathematics Subject Classification. Primary 53C20.
Key words and phrases. Manifold with boundary, Bakry-Émery Ricci curvature.

To the top of this page

Back to the Contents