A Model of the Teichmüller space of genus-zero bordered surfaces by period maps

2017/10/18 by Radnell, David, Schippers, Eric, Staubach, Wolfgang · 1 citation
#3062 #30C40 #30C55 #30F60 #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.1710.06960

Abstract

We consider Riemann surfaces Σ with n borders homeomorphic to \mathbbS¹ and no handles. Using generalized Grunsky operators, we define a period mapping from the infinite-dimensional Teichmüller space of surfaces of this type into the unit ball in the linear space of operators on an n-fold direct sum of Bergman spaces of the disk. We show that this period mapping is holomorphic and injective.

Cited by

• Scattering theory on Riemann surfaces II: The scattering matrix and generalized period mappings

Related

• DIFF(s¹), TeichmÜller Space and Period Matrices: Canonical Mappings via String Theory
• On the Teichmüller geodesic generated by the L-shaped translation surface tiled by three squares
• Visualizing the unit ball for the Teichmüller metric
• Teichmuller Space is Not Gromov Hyperbolic
• A convergent Weil-Petersson metric on the Teichmüller space of bordered Riemann surfaces