Abstract
|
|
The Teichmüller space of a closed oriented (real) surface of genus at least 2 is a
moduli space of complex structures on the surface, but can also be defined as a
space of certain representations of the fundamental group of the surface in
the group of orientation-preserving isometries of the hyperbolic plane. As a
consequence the tangent spaces of Teichmüller space admit two rather different
descriptions. We use harmonic vector fields (defined as infinitesimal analogs of
harmonic maps) on the hyperbolic plane to make a bridge between these
descriptions.
|
Keywords
Teichmüller space, harmonic, quadratic differential,
Poisson kernel
|
Mathematical Subject Classification
Primary: 30F60
|
Milestones
Received: 7 November 2024
Revised: 30 June 2025
Accepted: 30 June 2025
Published: 24 August 2025
|
| © 2025 MSP (Mathematical Sciences
Publishers). Distributed under the Creative Commons
Attribution License 4.0 (CC BY). |
Open Access made possible by participating
institutions via Subscribe to Open. 
|
