On the Martin Boundary of Rank 1 Manifolds with Nonpositive Curvature

被引：0
作者：
Ran Ji
机构：
[1] Tsinghua University,Yau Mathematical Sciences Center
来源：
The Journal of Geometric Analysis | 2019年 / 29卷
关键词：
Rank 1 manifold; Martin boundary; Nonpositive curvature; 58J32;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
For a manifold with nonpositive curvature, the Martin boundary is described by the behavior of normalized Green’s functions at infinity. A classical result by Anderson and Schoen states that if the manifold has pinched negative curvature, the geometric boundary is the same as the Martin boundary. In this paper, we study the Martin boundary of rank 1 manifolds admitting compact quotients. It is proved that a residual set in the geometric boundary can be identified naturally with a subset of the Martin boundary. This gives a partial answer to one of the open problems in geometry collected by Yau.
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页码：2805 / 2822
页数：17
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