TY - JOUR
T1 - Rigidity Phenomena in Manifolds with Boundary Under a Lower Weighted Ricci Curvature Bound
AU - Sakurai, Yohei
N1 - Publisher Copyright:
© 2018, Mathematica Josephina, Inc.
PY - 2019/1/15
Y1 - 2019/1/15
N2 - We study Riemannian manifolds with boundary under a lower N-weighted Ricci curvature bound for N at most 1, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude 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 N-weighted Ricci curvature bound for N at most 1, and under a lower weighted mean curvature bound for the boundary. We examine rigidity phenomena in such manifolds with boundary. We conclude 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 - Manifold with boundary
KW - Weighted Ricci curvature
KW - Weighted p-Laplacian
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U2 - 10.1007/s12220-017-9871-7
DO - 10.1007/s12220-017-9871-7
M3 - Article
AN - SCOPUS:85055947182
VL - 29
JO - Journal of Geometric Analysis
JF - Journal of Geometric Analysis
SN - 1050-6926
IS - 1
ER -