Incompleteness of pressure metric on Teichm\"uller space of a bordered surface
Dynamical Systems
2016-08-16 v1 Geometric Topology
Abstract
We prove that the pressure metric on the Teichm\"uller space of a bordered surface is incomplete and its partial completion can be given by the moduli space of metric graphs for a fat graph associated to the same bordered surface equipped with pressure metric. As a corollary, we show that the pressure metric is not a constant multiple of the Weil-Petersson metric which is different from the closed surface case.
Keywords
Cite
@article{arxiv.1608.03937,
title = {Incompleteness of pressure metric on Teichm\"uller space of a bordered surface},
author = {Binbin Xu},
journal= {arXiv preprint arXiv:1608.03937},
year = {2016}
}
Comments
17 pages, 8 figures