Regularity of harmonic maps into Teichmüller space

2025/09/05 by Yitong Sun, Sun, Yitong · 1 citation
Engineering · Mathematics · #58E20 (Primary) 53C43 #Advanced Numerical Analysis Techniques #Analytic and geometric function theory #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2509.05506

openalex publication_date 2025/09/05 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We prove a regularity theorem for harmonic maps into Teichmüller space. More specifically, if u is a harmonic map from a Riemannian domain to the metric completion of Teichmüller space with respect to the Weil-Petersson metric, and the image of u intersects a stratum of the augmented Teichmüller space, then u is entirely contained in this stratum. This extends Wolpert's result on the geodesic convexity of the augmented Teichmüller space to higher dimensions and generalizes the regularity result of Daskalopoulos and Mese by showing that the singular set of u is empty.

Citations

• Harmonic Maps and Teichmueller Theory
• The Weil-Petersson metric and volumes of 3-dimensional hyperbolic convex cores
• The moduli space of Riemann surfaces is Kahler hyperbolic

Cited by

• Harmonic maps in singular geometry and rigidity

Related

• Rigidity of Teichmuller Space
• On Harmonic Mappings into Weil-Peterssson Completed Teichmuller Spaces
• The harmonic maps compactification of Teichmüller spaces for punctured Riemann surfaces
• Comments on the regularity of harmonic maps between singular spaces
• Partial regularity of harmonic maps from Alexandrov spaces