Geodesic
There are no exotic ladder surfaces
Ara Basmajian1 ; Nicholas G. Vlamis2
1 City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Hunter College, Department of Mathematics
2 City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Queens College, Department of Mathematics
Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1007-1023

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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).
Keywords: Quasiconformal mappings, quasiconformal homogeneity, Riemann surfaces, infinite-type surfaces

Ara Basmajian 1 ; Nicholas G. Vlamis 2

1 City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Hunter College, Department of Mathematics
2 City University of New York, The Graduate Center, Department of Mathematics; and City University of New York, Queens College, Department of Mathematics 
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Ara Basmajian; Nicholas G. Vlamis. There are no exotic ladder surfaces. Annales Fennici Mathematici, Tome 47 (2022) no. 2, pp. 1007-1023. http://geodesic.mathdoc.fr/item/AFM_2022_47_2_a18/