Harmonic maps to Teichmüller space

Georgios Daskalopoulos; Ludmil Katzarkov; Richard Wentworth

doi:10.4310/MRL.2000.v7.n1.a12

Harmonic maps to Teichmüller space

Georgios Daskalopoulos, Ludmil Katzarkov, Richard Wentworth

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

Abstract

We give sufficient conditions for the existence of equivariant harmonic maps from the universal cover of a Riemann surface B to the Teichmüller space of a genus g ≥ 2 surface ∑. The condition is in terms of the representation of the fundamental group of B to the mapping class group of ∑. The metric on Teichmüller space is chosen to be the Kähler hyperbolic metric. Examples of such representations arise from symplectic Lefschetz fibrations.

Original language	English (US)
Pages (from-to)	133-146
Number of pages	14
Journal	Mathematical Research Letters
Volume	7
Issue number	1
DOIs	https://doi.org/10.4310/MRL.2000.v7.n1.a12
State	Published - 2000
Externally published	Yes

ASJC Scopus subject areas

Mathematics(all)

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abstract = "We give sufficient conditions for the existence of equivariant harmonic maps from the universal cover of a Riemann surface B to the Teichm{\"u}ller space of a genus g ≥ 2 surface ∑. The condition is in terms of the representation of the fundamental group of B to the mapping class group of ∑. The metric on Teichm{\"u}ller space is chosen to be the K{\"a}hler hyperbolic metric. Examples of such representations arise from symplectic Lefschetz fibrations.",

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AB - We give sufficient conditions for the existence of equivariant harmonic maps from the universal cover of a Riemann surface B to the Teichmüller space of a genus g ≥ 2 surface ∑. The condition is in terms of the representation of the fundamental group of B to the mapping class group of ∑. The metric on Teichmüller space is chosen to be the Kähler hyperbolic metric. Examples of such representations arise from symplectic Lefschetz fibrations.

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