# Convergence of Siegel–Veech constants

@article{Dozier2016ConvergenceOS,
title={Convergence of Siegel–Veech constants},
author={Benjamin Dozier},
journal={Geometriae Dedicata},
year={2016},
volume={198},
pages={131-142}
}
• B. Dozier
• Published 31 December 2016
• Mathematics
• Geometriae Dedicata
We show that for any weakly convergent sequence of ergodic $$SL_2(\mathbb {R})$$SL2(R)-invariant probability measures on a stratum of unit-area translation surfaces, the corresponding Siegel–Veech constants converge to the Siegel–Veech constant of the limit measure. Together with a measure equidistribution result due to Eskin–Mirzakhani–Mohammadi, this yields the (previously conjectured) convergence of sequences of Siegel–Veech constants associated to Teichmüller curves in genus two. The proof…
• B. Dozier
• Mathematics
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