Local rigidity of Schottky maps
Metric Geometry
2013-05-22 v1
Abstract
We introduce Schottky maps-conformal maps between relative Schottky sets, and study their local rigidity properties. This continues the investigations of relative Schottky sets initiated in [S. Merenkov, "Planar relative Schottky sets and quasisymmetric maps", Proc. London Math. Soc. (3) 104 (2012), 455-485]. Besides being of independent interest, the latter and current works provide key ingredients in the forthcoming proof of quasisymmetric rigidity of Sierpi\'nski carpet Julia sets of rational functions.
Cite
@article{arxiv.1305.4683,
title = {Local rigidity of Schottky maps},
author = {Sergei Merenkov},
journal= {arXiv preprint arXiv:1305.4683},
year = {2013}
}
Comments
16 pages