Comparing hyperbolic and extremal lengths for shortest curves
Geometric Topology
2025-09-18 v2 Differential Geometry
Abstract
We give a lower bound for the widths of the collars of certain short partial pants decomposition of the surface. Then we apply this to obtain upper bounds of the renormalized volume of certain Schottky manifolds in terms of the hyperbolic length of compressible curves.
Cite
@article{arxiv.1911.09078,
title = {Comparing hyperbolic and extremal lengths for shortest curves},
author = {Dídac Martínez-Granado and Franco Vargas Pallete},
journal= {arXiv preprint arXiv:1911.09078},
year = {2025}
}
Comments
Updated version. Sections 3 and 4 were merged, while Section 6 was removed. Statement of the main result and application were adjusted. 20 pages, 7 figures. Comments are welcome!