Comparing hyperbolic and extremal lengths for shortest curves

2019/11/20 by Dídac Martínez‐Granado, Martínez-Granado, Dídac, Franco Vargas Pallete +1 · 1 citation
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1911.09078

openalex publication_date 2019/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• On the renormalized volume of hyperbolic 3-manifolds
• Upper bounds on Renormalized Volume for Schottky groups

Cited by

• The extremal length systole of the Bolza surface

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