PreprintCC BY-NC-ND 4.0arXiv
Volume of area-bounded PGL3-Hitchin moduli space
Abstract
For the PGL3-Hitchin moduli space of unmarked convex ℝℙ2 structures on the surface Sg,m with fixed boundary data 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 Cg,m(t+λ2)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·Area-weighted volume.
Related
- The Thick Part of the PSLn(ℝ)-Hitchin-Riemann Moduli Space has Infinite Volume
- On the Asymptotics of the Volume of Hitchin Moduli Spaces
- Localization of weighted Goldman volume on SL(3,R)-Hitchin Component
- Tremors and horocycle dynamics on the moduli space of transition surfaces
- Triangles minimize the Monge-Ampère eigenvalue among planar bounded convex domains of a given area
BibTeX
@misc{li2026volume,
title = {{Volume of area-bounded PGL3-Hitchin moduli space}},
author = {Qiongling Li and Beibei Liu and Weixu Su and Zhe Sun},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33417},
eprint = {2610.33417},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33417},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Volume of area-bounded PGL3-Hitchin moduli space
AU - Qiongling Li
AU - Beibei Liu
AU - Weixu Su
AU - Zhe Sun
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2610.33417
UR - https://arxiv.org/abs/2610.33417
AB - For the PGL_3-Hitchin moduli space of unmarked convex ℝℙ^2 structures on the surface S_g,m with fixed boundary data 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·Area-weighted volume.
ER -