Abstract
Let M be a closed Riemann surface, N a Riemannian manifold of Hermitian non-positive curvature, f : M → N a continuous map, and E the function on the Teichmüller space of M that assigns to a complex structure on M the energy of the harmonic map homotopic to f. We show that E is a plurisubharmonic function on the Teichmüller space of M. If N has strictly negative Hermitian curvature, we characterize the directions in which the complex Hessian of E vanishes.
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Author partially supported by NSF grants DMS 0200877 and DMS-0600816.
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Toledo, D. Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space. Geom. Funct. Anal. 22, 1015–1032 (2012). https://doi.org/10.1007/s00039-012-0185-4
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DOI: https://doi.org/10.1007/s00039-012-0185-4