Annals of Global Analysis and Geometry

, Volume 55, Issue 3, pp 479–507 | Cite as

Holomorphic quadratic differentials dual to Fenchel–Nielsen coordinates

  • Nadine GroßeEmail author
  • Melanie Rupflin


We discuss bases of the space of holomorphic quadratic differentials that are dual to the differentials of Fenchel–Nielsen coordinates and hence appear naturally when considering functions on the set of hyperbolic metrics which are invariant under pull-back by diffeomorphisms, such as eigenvalues of the Laplacian. The precise estimates derived in the current paper form the basis for the proof of the sharp eigenvalue estimates on degenerating surfaces obtained by the authors in another paper.


Geometric analysis Functions on degenerating hyperbolic surfaces Fenchel–Nielsen coordinates 


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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität FreiburgFreiburgGermany
  2. 2.Mathematical InstituteUniversity of OxfordOxfordUK

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