English

Holomorphic quadratic differentials dual to Fenchel-Nielsen coordinates

Differential Geometry 2018-12-18 v2

Abstract

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 in arXiv:1701.08491.

Keywords

Cite

@article{arxiv.1806.04384,
  title  = {Holomorphic quadratic differentials dual to Fenchel-Nielsen coordinates},
  author = {Nadine Große and Melanie Rupflin},
  journal= {arXiv preprint arXiv:1806.04384},
  year   = {2018}
}

Comments

Consists mostly of Section 4 of the previous version of the preprint arXiv:1701.08491 which was split up for easier publication