Abstract
In this paper, we show that the extremal length functions on Teichmuller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of L.Liu and this http URL's results on the plurisubharmonicity of extremal length functions. We also obtain alternative proofs of S.Krushkal's results that a function defined by the Teichmuller distance from a reference point is plurisubharmonic, and the Teichmuller space is hyperconvex. To show the log-plurisubharmonicity, we give an explicit formula of the Levi form of the extremal length functions in generic case.
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