论文标题
liouville量子重力表面的地球网络
Geodesic networks in Liouville quantum gravity surfaces
论文作者
论文摘要
最近的工作表明，对于$γ\，在（0,2）$中，Liouville量子重力（LQG）表面可以赋予规范度量。我们证明了有关该指标的测量学的几个结果。特别是，我们将可能的大地测量网络从表面上的典型点到表面上的任意点进行分类，以及地表学上有两个点的测量线网络类型，这些点是表面上密集的一对点。后一个结果是由于Angel，Kolesnik和Miermont（2017）而导致的Brownian Map中的$γ$ -LQG类似物的分类。我们还表明，有一个确定性的$ m \ in \ mathbb n $，因此几乎可以肯定的是，最多有两个点由$ m $ m $不同的LQG Geodesics加入。
Recent work has shown that for $γ\in (0,2)$, a Liouville quantum gravity (LQG) surface can be endowed with a canonical metric. We prove several results concerning geodesics for this metric. In particular, we completely classify the possible networks of geodesics from a typical point on the surface to an arbitrary point on the surface, as well as the types of networks of geodesics joining two points which occur for a dense set of pairs of points on the surface. This latter result is the $γ$-LQG analog of the classification of geodesic networks in the Brownian map due to Angel, Kolesnik, and Miermont (2017). We also show that there is a deterministic $m\in\mathbb N$ such that almost surely any two points are joined by at most $m$ distinct LQG geodesics.
