Year: 2022
Type: preprint
Abstract: We work with the space $\mathcal C(S)$ of geodesic currents on a closed surface $S$ of negative Euler characteristic. By prior work of the author with Sebastian Hensel, each filling geodesic current $μ$ has a unique length-minimizing metric $X$ in Teichmüller space. In this paper, we show that, on so-called thick components of $X$, the geometries of $μ$ and $X$ are comparable, up to a scalar depending only on $μ$ and the topology of $S$. We also characterize thick components of the projection using only the length function of $μ$.
Source: arXiv (Cornell University)
Author: Sapir, Jenya
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4302012795