Holomorphic quadratic differentials in Teichmüller theory
arXiv:1902.06406
Abstract
This expository survey describes how holomorphic quadratic differentials arise in several aspects of Teichmüller theory, highlighting their relation with various geometric structures on surfaces. The final section summarizes results for non-compact surfaces of finite type, when the quadratic differential has poles of finite order at the punctures.
33 pages, 6 figures, to appear in the Handbook of Teichmüller Theory Vol VII