On the Existence of Jenkins-Strebel Differentials Using Harmonic Maps from Surfaces to Graphs

1994/06/29 by Michael Wolf, Wolf, Michael · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9406003

8 pages, 2 figures available upon request

arxiv created 1994/06/29 · openalex publication_date 1994/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a new proof of the existence (\citeHM, \citeRen) of a Jenkins-Strebel differential Φ on a Riemann surface \SR with prescribed heights of cylinders by considering the harmonic map from \SR to the leaf space of the vertical foliation of Φ, thought of as a Riemannian graph. The novelty of the argument is that it is essentially Riemannian as well as elementary; moreover, the harmonic maps existence theory on which it relies is classical, due mostly to Morrey (\citeMo).

Cited by

• On the non-Archimedean Hitchin map for SL₂(F)
• The Schwarzian derivative and measured laminations on Riemann surfaces

Related

• Jenkins-Strebel Differentials on the Riemann Sphere with Four Simple Poles
• Quadratic differentials, half-plane structures, and harmonic maps to graphs
• The distribution of critical graphs of Jenkins-Strebel differentials
• The surface of circumferences for Jenkins-Strebel differentials
• Explicit Examples of Strebel Differentials