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- Title
The Harmonic Map Compactification of Teichm\"{u}ller Spaces for Punctured Riemann Surfaces.
- Authors
Sakai, Kento
- Abstract
In the paper [ The Teichmüller theory of harmonic maps , J. Differential Geom. 29 (1989), no. 2, 449–479], Wolf provided a global coordinate system of the Teichmüller space of a closed oriented surface S with the vector space of holomorphic quadratic differentials on a Riemann surface X homeomorphic to S. This coordinate system is via harmonic maps from the Riemann surface X to hyperbolic surfaces. Moreover, he gave a compactification of the Teichmüller space by adding a point at infinity to each endpoint of harmonic map rays starting from X in the space. Wolf also showed this compactification coincides with the Thurston compactification. In this paper, we extend the harmonic map ray compactification to the case of punctured Riemann surfaces and show that it still coincides with the Thurston compactification.
- Subjects
RIEMANN surfaces; TEICHMULLER spaces; HARMONIC maps; QUADRATIC differentials; VECTOR spaces; COMMERCIAL space ventures
- Publication
Conformal Geometry & Dynamics, 2023, Vol 27, p322
- ISSN
1088-4173
- Publication type
Article
- DOI
10.1090/ecgd/388