Variation of extremal length functions on Teichmuller space

Lixin Liu; Weixu Su

doi:10.1093/imrn/rnw196

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arXiv · 1210.0743

Variation of extremal length functions on Teichmuller space

Lixin Liu·Weixu Su

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Abstract

Extremal length is an important conformal invariant on Riemann surface. It is closely related to the geometry of Teichmuller metric on Teichmuller space. By identifying extremal length functions with energy of harmonic maps from Riemann surfaces to $\mathbb{R}$-trees, we study the second variation of extremal length functions along Weil-Petersson geodesics. We show that the extremal length of any measured foliation is a pluri-subharmonic function on Teichmuller space.

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BibTeX RIS

Lixin Liu, Weixu Su. 2016-08-27. Variation of extremal length functions on Teichmuller space. https://doi.org/10.1093/imrn%2Frnw196

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