论文标题
未标记有限的正凸的模量空间的体积
Volume of the moduli space of unmarked bounded positive convex $\mathbb{RP}^2$ structures
论文作者
论文摘要
对于未标记的凸$ \ mathbb {rp}^2 $结构的模量空间，表面$ s_ {g，m} $具有负极特征，我们调查了模量空间的子集，该概念由诸如投影型不变性，gromov bolicality strangity comment，quasicis inf sherce necters necters necters necters等概述所定义的概念定义。我们表明，该子集的高盛符号量与某些投影不变的在上面的投影不变式和固定边界简单的根长度$ \ mathbf {l} $在上面由$（t，\ mathbf {l}）的积极多项式限制，因此所有其他子集的体积都是有限的。我们表明，Mumford的紧凑度定理的类似物对于该区域有限的子集。
For the moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with negative Euler characteristic, we investigate the subsets of the moduli space defined by the notions like boundedness of projective invariants, area, Gromov hyperbolicity constant, quasisymmetricity constant etc. These subsets are comparable to each other. We show that the Goldman symplectic volume of the subset with certain projective invariants bounded above by $t$ and fixed boundary simple root lengths $\mathbf{L}$ is bounded above by a positive polynomial of $(t,\mathbf{L})$ and thus the volume of all the other subsets are finite. We show that the analog of Mumford's compactness theorem holds for the area bounded subset.
