论文标题
liouville量子重力度量的Minkowski内容度量
The Minkowski content measure for the Liouville quantum gravity metric
论文作者
论文摘要
liouville量子重力（LQG）表面是自然的随机二维表面，最初是作为随机测量空间配制的，后来作为随机度量空间。我们表明，LQG度量可以作为Minkowski量度相对于LQG度量的措施回收，回答了Gwynne和Miller的问题（Arxiv：1905.00383）。结果，我们证明了$γ$ -LQG表面的度量结构决定了其（0,2）$中每个$γ\的共形结构。我们的主要工具是用于空间填充SLE的连续交配理论。在证明的过程中，我们还建立了相对于LQG度量的空间填充SLE的Hölder连续性结果。
A Liouville quantum gravity (LQG) surface is a natural random two-dimensional surface, initially formulated as a random measure space and later as a random metric space. We show that the LQG measure can be recovered as the Minkowski measure with respect to the LQG metric, answering a question of Gwynne and Miller (arXiv:1905.00383). As a consequence, we prove that the metric structure of a $γ$-LQG surface determines its conformal structure for every $γ\in (0,2)$. Our primary tool is the continuum mating-of-trees theory for space-filling SLE. In the course of our proof, we also establish a Hölder continuity result for space-filling SLE with respect to the LQG metric.
