TY - JOUR
T1 - Rigidity of manifolds with boundary under a lower bakry-& mery ricci curvature bound
AU - Sakurai, Yohei
N1 - Publisher Copyright:
© 2019 Tohoku Mathematical Journal. All Rights Reserved.
PY - 2019/3
Y1 - 2019/3
N2 - We study Riemannian manifolds with boundary under a lower Bakry- Emery 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.
AB - We study Riemannian manifolds with boundary under a lower Bakry- Emery 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.
KW - Bakry-emery ricci curvature
KW - Manifold with boundary
UR - http://www.scopus.com/inward/record.url?scp=85064340955&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85064340955&partnerID=8YFLogxK
U2 - 10.2748/tmj/1552100443
DO - 10.2748/tmj/1552100443
M3 - Article
AN - SCOPUS:85064340955
VL - 71
SP - 69
EP - 109
JO - Tohoku Mathematical Journal
JF - Tohoku Mathematical Journal
SN - 0040-8735
IS - 1
ER -