Comparing hyperbolic and extremal lengths for shortest curves

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.

Final version accepted for publication at Algebraic & Geometric Topology. Typos corrected. 20 pages, 7 figures. Comments are welcome!

References in corpus (3)

• On the renormalized volume of hyperbolic 3-manifolds
• Additive continuity of the renormalized volume under geometric limits
• Upper bounds on Renormalized Volume for Schottky groups

Cited by in corpus (1)

• The extremal length systole of the Bolza surface