Variation of extremal length functions on Teichmuller space
Geometric Topology
2016-08-30 v3
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 -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.
Keywords
Cite
@article{arxiv.1210.0743,
title = {Variation of extremal length functions on Teichmuller space},
author = {Lixin Liu and Weixu Su},
journal= {arXiv preprint arXiv:1210.0743},
year = {2016}
}
Comments
New version (v3): 27 pages, 3 figures. The main theorem (on pluri-subharmonicity of extremal length functions) is modified and the proofs are clarified. Accepted for publication in the journal International Mathematics Research Notices