Rigidity for the isoperimetric inequality of negative effective dimension on weighted Riemannian manifolds
Rigidity for the isoperimetric inequality of negative effective dimension on weighted Riemannian manifolds
复制标题
DOI：
10.1007/s10711-018-0410-x
复制
发表时间：
2017-12
影响因子：
0.5
通讯作者：
Cong Hung Mai
中科院分区：
文献类型：
--
作者：
Cong Hung Mai
我们在加权黎曼流形上研究了当等式在等周不等式中成立时。我们的主要定理断言，这样的流形必然等距于双曲性的翘曲积，其中存在一个具有较低加权Ricci曲率界的维流形，并且配备了双曲余弦测度。这是一个类似于庞加莱不等条件的现象。此外，每个等周极小值集在适当的意义下都是等距于半空间的。
We study, on a weighted Riemannian manifold offor, when equality holds in the isoperimetric inequality. Our main theorem asserts that such a manifold is necessarily isometric to the warped productof hyperbolic nature, whereis an-dimensional manifold with lower weighted Ricci curvature bound andis equipped with a hyperbolic cosine measure. This is a similar phenomenon to the equality condition of Poincaré inequality. Moreover, every isoperimetric minimizer set is isometric to a half-space in an appropriate sense.