Local Rigidity of Teichm\"uller space with Thurston metric
Geometric Topology
2023-01-27 v3 Complex Variables
Differential Geometry
Abstract
We show that every -linear surjective isometry between the cotangent spaces to the Teichm\"uller space equipped with the Thurston norm is induced by some isometry between the underlying hyperbolic surfaces, which is an analogue of Royden's theorem concerning the Teichm\"uller metric.
Keywords
Cite
@article{arxiv.2005.11762,
title = {Local Rigidity of Teichm\"uller space with Thurston metric},
author = {Huiping Pan},
journal= {arXiv preprint arXiv:2005.11762},
year = {2023}
}
Comments
Final version, minor revision according to referee's report. To appear in Science China Mathematics