Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound
Rigidity of manifolds with boundary under a lower Bakry-Émery Ricci curvature bound
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DOI：
10.2748/tmj/1552100443
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发表时间：
2015-06
影响因子：
0.5
通讯作者：
Y. Sakurai
中科院分区：
文献类型：
--
作者：
Y. Sakurai
研究了边界在Bakry-E 'mery Ricci曲率下界下的黎曼流形。在我们的加权设置，我们证明了几个刚性定理，这样的流形的边界。我们得出一个刚性定理的内接半径，体积增长刚性定理的度量邻域的边界，和各种分裂定理。我们也得到了刚性的结果，最小的Dirichlet特征值的加权p-Laplacian。
We study Riemannian manifolds with boundary under a lower Bakry-E'mery 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 results for the smallest Dirichlet eigenvalues for the weighted p-Laplacians.