# Plurisuperharmonicity of reciprocal energy function on Teichmüller space and Weil-Petersson metric

@article{Kim2019PlurisuperharmonicityOR, title={Plurisuperharmonicity of reciprocal energy function on Teichm{\"u}ller space and Weil-Petersson metric}, author={Inkang Kim and Xueyuan Wan and Genkai Zhang}, journal={arXiv: Differential Geometry}, year={2019} }

We consider harmonic maps$u(z): \mathcal{X}_z\to N$ in a fixed homotopy class from Riemann surfaces $\mathcal{X}_z$ of genus $g\geq 2$ varying in the Teichmu{}ller space $\mathcal T$ to a Riemannian manifold $N$ with non-positive Hermitian sectional curvature.
The energy function $E(z)=E(u(z))$ can be viewed as a function on $\mathcal T$ and we study its first and the second variations. We prove that the reciprocal energy function $E(z)^{-1}$ is plurisuperharmonic on Teichmuller space. We also… Expand

#### 3 Citations

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