There are no exotic ladder surfaces

TL;DR

This paper addresses the open problem of characterizing quasiconformally homogeneous Riemann surfaces, proving that all ladder surfaces are equivalent to regular covers of closed surfaces, thus ruling out exotic examples.

Contribution

It provides a characterization of quasiconformally homogeneous ladder surfaces, showing they are all regular covers of closed surfaces, resolving a specific open case.

Findings

All quasiconformally homogeneous ladder surfaces are regular covers of closed surfaces.

The problem of characterizing such surfaces can be reduced to four open cases.

No exotic ladder surfaces exist within the studied class.

Abstract

It is an open problem to provide a characterization of quasiconformally homogeneous Riemann surfaces. We show that given the current literature, this problem can be broken into four open cases with respect to the topology of the underlying surface. The main result is a characterization in one of the these open cases; in particular, we prove that every quasiconformally homogeneous ladder surface is quasiconformally equivalent to a regular cover of a closed surface (or, in other words, there are no exotic ladder surfaces).