Geodesic networks in Liouville quantum gravity surfaces

Recent work has shown that for $\gamma \in (0,2)$, a Liouville quantum gravity (LQG) surface can be endowed with canonical metric. We prove several results concerning geodesics this In particular, we completely classify the possible networks of from typical point on to an arbitrary surface, as well types joining two points which occur dense set pairs surface. This latter result is $\gamma$-LQG analog classification geodesic in Brownian map due Angel, Kolesnik, and Miermont (2017). also show there deterministic $m\in\mathbb N$ such almost surely any are joined by at most $m$ distinct LQG geodesics.