Macroscopic scalar curvature and areas of cycles
Macroscopic scalar curvature and areas of cycles
复制标题
宏观标量曲率和循环面积
DOI：
10.1007/s00039-017-0417-8
复制
发表时间：
2017
影响因子：
2.2
通讯作者：
Hannah Alpert and Kei Funano
中科院分区：
文献类型：
--
作者：
Kei Funano and Yohei Sakurai;Hannah Alpert and Kei Funano
在本文中，我们证明了以下内容。设是n维闭双曲流形，设g是上的黎曼度量，给定黎曼泛覆盖中单位球体积的一个上界，我们得到-同调类面积的一个下界，它正比于上的双曲面积。该定理是基于一个定理的Guth和类似的定理的Kronheimer和Mrowka涉及标量曲率。
In this paper we prove the following. Letbe ann–dimensional closed hyperbolic manifold and letgbe a Riemannian metric on. Given an upper bound on the volumes of unit balls in the Riemannian universal cover, we get a lower bound on the area of the–homology classon, proportional to the hyperbolic area of. The theorem is based on a theorem of Guth and is analogous to a theorem of Kronheimer and Mrowka involving scalar curvature.