Extremal length functions are log-plurisubharmonic

Hideki Miyachi

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arXiv · 1505.06785

Extremal length functions are log-plurisubharmonic

Hideki Miyachi

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Abstract

In this paper, we show that the extremal length functions on Teichm\"uller space are log-plurisubharmonic. As a corollary, we obtain an alternative proof of L.Liu and W.Su'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 Teichm\"uller distance from a reference point is plurisubharmonic, and the Teichm\"uller 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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Hideki Miyachi. 2015-05-26. Extremal length functions are log-plurisubharmonic. https://arxiv.org/abs/1505.06785

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