Harmonic Maps to Teichmüller Space
نویسندگان
چکیده
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 Σ. The condition is in terms of the representation of the fundamental group of B to the mapping class group of Σ. The metric on Teichmüller space is chosen to be the Kähler hyperbolic metric. Examples of such representations arise from symplectic Lefschetz fibrations. Date: January 30, 2000 (final revision). 1991 Mathematics Subject Classification. Primary: 58E20 ; Secondary: 32G13, 30F60, 57M60. G.D. supported in part by NSF grant DMS-9803606. L.K. supported in part by NSF grant DMS-9700605 and a Sloan Research Fellowship. R.W. supported in part by NSF grant DMS-9971860.
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