发表机构
Courant Institute of Mathematical Sciences, New York University（纽约大学柯朗数学科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该数学研究证明次临界γ-LQG度量依律收敛于临界2-LQG度量，结合相关成果得到γ-LQG度量的律在γ∈[0,2]上关于γ连续的结论。
AI 中文摘要
我们证明，对于γ∈(0,2)的γ-LQG度量（经适当重标），在复平面C×C上连续函数的局部一致拓扑下，依律收敛于经适当重标的临界2-LQG度量。结合arXiv:2509.15544的结果，可得γ∈[0,2]时，γ-LQG度量（经适当重标）的律在C×C上连续函数的局部一致拓扑下关于γ连续，其中0-LQG度量对应C上的欧氏度量。
英文摘要
We show that the $γ$-LQG metric (appropriately re-normalized) for $γ\in (0,2)$ converges in law to the critical 2-LQG metric (appropriately re-normalized) with respect to the local uniform topology of continuous functions on $\mathbb{C} \times \mathbb{C}$. Combining with the results in arXiv:2509.15544, we obtain that the law of the $γ$-LQG metric (appropriately re-normalized) is continuous in $γ\in [0,2]$ with respect to the local uniform topology of continuous functions on $\mathbb{C} \times \mathbb{C}$, where the 0-LQG metric corresponds to the Euclidean metric on $\mathbb{C}$.
