Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound

Yohei Sakurai

Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound

Differential Geometry 2017-05-22 v2

Authors: Yohei Sakurai

Abstract

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.

Keywords

riemannian manifolds with boundary weighted ricci curvature rigidity phenomena volume growth rigidity splitting theorem dirichlet eigenvalue weighted p-laplacian

Cite

@article{arxiv.1605.02493,
  title  = {Rigidity phenomena in manifolds with boundary under a lower weighted Ricci curvature bound},
  author = {Yohei Sakurai},
  journal= {arXiv preprint arXiv:1605.02493},
  year   = {2017}
}

Comments

34 pages. arXiv admin note: text overlap with arXiv:1506.03223

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