Grafting, harmonic maps, and projective structures on surfaces

1995/08/14 by Harumi Tanigawa, Tanigawa, Harumi
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.math/9508216

openalex publication_date 1995/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Grafting is a surgery on Riemann surfaces introduced by Thurston which connects hyperbolic geometry and the theory of projective structures on surfaces. We will discuss the space of projective structures in terms of the Thurston's geometric parametrization given by grafting. From this approach we will prove that on any compact Riemann surface with genus greater than 1 there exist infinitely many projective structures with Fuchsian holonomy representations. In course of the proof it will turn out that grafting is closely related to harmonic maps between surfaces.

Related

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• The grafting map of Teichmuller space
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