Degeneration of hyperbolic surfaces from the viewpoint of harmonic maps

G2T2 Seminar

Organizer：

G2T2 Group

Speaker：

Kento Sakai (Tokyo University)

Time：

Friday, 10:00-11:30 am

Dec 19, 2025

Venue：

Ningzhai (宁斋) 203

Title：

Degeneration of hyperbolic surfaces from the viewpoint of harmonic maps

Abstract:

The Teichmüller space is the space of isotopy classes of hyperbolic structures on a topological surface. Wolf parametrized the Teichmüller space by the space of holomorphic quadratic differentials on a Riemann surface, using harmonic maps from the Riemann surface to hyperbolic surfaces. This parametrization extends naturally to the boundary of the Thurston compactification of the Teichmüller space, and therefore the harmonic map approach provides a means to degenerations of hyperbolic surfaces. Recently, analogues of this parametrization have been developed for hyperbolic surfaces with cusps and boundaries.

In this talk, I will introduce the harmonic map parametrization and discuss several results concerning the degeneration of hyperbolic surfaces.