There are no exotic ladder surfaces

Authors

  • Ara Basmajian City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Hunter College, Department of Mathematics
  • Nicholas G. Vlamis City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Queens College, Department of Mathematics

Keywords:

Quasiconformal mappings, quasiconformal homogeneity, Riemann surfaces, infinite-type surfaces

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 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).
Issue
Vol. 47 No. 2 (2022)
Section
Articles

Published

2022-07-12

How to Cite

Basmajian, A., & Vlamis, N. G. (2022). There are no exotic ladder surfaces. Annales Fennici Mathematici, 47(2), 1007–1023. Retrieved from https://afm.journal.fi/article/view/120592

Copyright (c) 2022 Annales Fennici Mathematici

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