Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

Details Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space Hermitian Curvature and Plurisubharmonicity of Energy on Teichmüller Space

2011-04-10

arxiv.org/abs/1104.1786v2

Mathematics

Differential Geometry

Revised version incorporating suggestions by the referees. To appear in GAFA

Scientific paper

Let $M$ be a closed Riemann surface, $N$ a Riemannian manifold of Hermitian non-positive curvature, $f:M\to N$ a continuous map, and $E$ the function on the Teichm\"uller 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 Teichm\"uller 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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