Year: 2026
Type: preprint
Abstract: For the $\mathrm{PGL}_3$-Hitchin moduli space of unmarked convex $\mathbb{RP}^2$ structures on the surface $S_{g,m}$ with fixed boundary data $\mathbf L$ when $m>0$, we investigate the subset whose canonical Hilbert--Busemann area is bounded above by $t$. We show that the Goldman symplectic volume of this subset is at most $C_{g,m}(t+λ^2)^{8g-8+3m}$, where $λ$ is the largest total-root boundary length for $m>0$ and is set to $0$ for $m=0$. As a consequence, We obtain the explicit upper bound for the $e^{-s\cdot\mathrm{Area}}$-weighted volume.
Source: arXiv (Cornell University)
Authors: Li, Qiongling, Liu, Beibei, Su, Weixu, Sun, Zhe
Institutions: Nankai University, The Ohio State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1217869746, G6927478418
OpenAlex ID: W7224003905