2021/04/13 by Jian Ding, Ewain Gwynne, Ding, Jian +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Geometry and complex manifolds #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2104.06502
openalex publication_date 2021/04/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let h be the planar Gaussian free field and let Dh be a supercritical Liouville quantum gravity (LQG) metric associated with h. Such metrics arise as subsequential scaling limits of supercritical Liouville first passage percolation (Ding-Gwynne, 2020) and correspond to values of the matter central charge c\mathrm M ∈ (1,25). We show that a.s. the boundary of each complementary connected component of a Dh-metric ball is a Jordan curve and is compact and finite-dimensional with respect to Dh. This is in contrast to the whole boundary of the Dh-metric ball, which is non-compact and infinite-dimensional with respect to Dh (Pfeffer, 2021). Using our regularity results for boundaries of complementary connected components of Dh-metric balls, we extend the confluence of geodesics results of Gwynne-Miller (2019) to the case of supercritical Liouville quantum gravity. These results show that two Dh-geodesics with the same starting point and different target points coincide for a non-trivial initial time interval.