Comparing hyperbolic and extremal lengths for shortest curves
arXiv:1911.09078
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.
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!