论文标题
马丁边界中摩尔斯边界的嵌入
An embedding of the Morse boundary in the Martin boundary
论文作者
论文摘要
我们从分层双曲线群的摩尔斯边界到其马丁边界构建了一对一的连续图。该构建是基于将Ancona在双曲线群上概括的偏离不平等基础。这为此类群体的Morse边界提供了一种可能的新型拓扑。我们还证明，除非该组是双曲线，否则摩尔斯边界对谐波测度的量度为0。
We construct a one-to-one continuous map from the Morse boundary of a hierarchically hyperbolic group to its Martin boundary. This construction is based on deviation inequalities generalizing Ancona's work on hyperbolic groups. This provides a possibly new metrizable topology on the Morse boundary of such groups. We also prove that the Morse boundary has measure 0 with respect to the harmonic measure unless the group is hyperbolic.
