Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

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 f...

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Bibliographic Details
Published in:Geometric and functional analysis 2012-08, Vol.22 (4), p.1015-1032
Main Author: Toledo, Domingo
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-012-0185-4