论文标题
liouville量子重力中的谐波球
Harmonic balls in Liouville quantum gravity
论文作者
论文摘要
谐波球是满足谐波函数均值属性的域。我们使用Hele-shaw流的障碍物问题表述，在Liouville量子重力（LQG）表面上建立了谐波球的存在和独特性。我们表明，LQG谐波球既不是Lipschitz域也不是LQG公制球，并且其互补相连的组件的边界是Jordan Curves。 我们猜想LQG谐波球是随机平面图上内部扩散限制聚集（IDLA）的缩放限制。在伴侣论文中，我们在配对crt地图的特殊情况下证明了这一点。
Harmonic balls are domains which satisfy the mean-value property for harmonic functions. We establish the existence and uniqueness of harmonic balls on Liouville quantum gravity (LQG) surfaces using the obstacle problem formulation of Hele-Shaw flow. We show that LQG harmonic balls are neither Lipschitz domains nor LQG metric balls, and that the boundaries of their complementary connected components are Jordan curves. We conjecture that LQG harmonic balls are the scaling limit of internal diffusion limited aggregation (IDLA) on random planar maps. In a companion paper, we prove this in the special case of mated-CRT maps.
