Quasi-isometric embeddings for shrinking maps from surfaces into the moduli space
Geometric Topology
2025-11-13 v1 Metric Geometry
Abstract
We investigate shrinking maps from a cusped hyperbolic surface into the moduli space of closed Riemann surfaces. For such a map and its lift to the Teichm\"uller space, we consider whether they are quasi-isometric embeddings with respect to natural metrics like the Teichm\"uller distance and the intrinsic distance. Under a mild condition, we prove that these properties are characterised solely by the map's monodromy. These characterisations apply, in particular, to holomorphic maps.
Cite
@article{arxiv.2511.09317,
title = {Quasi-isometric embeddings for shrinking maps from surfaces into the moduli space},
author = {Yibo Zhang},
journal= {arXiv preprint arXiv:2511.09317},
year = {2025}
}
Comments
17p., 1 figure