Volumes of the sets of translation surfaces with small saddle connections in rank one affine submanifolds

Abstract

We prove some estimates of the volumes of the sets of translation surfaces of unit area having several independent small saddle connections in a rank one affine submanifold.

The paper has been completely rewritten, the results of the previous versions are now in the appendices

References in corpus (4)

• Invariant and stationary measures for the SL(2,R) action on Moduli space
• Periodic geodesics on translation surfaces
• Complete periodicity of Prym eigenforms
• SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular

Cited by in corpus (3)

• Measure bound for translation surfaces with short saddle connections
• SL(2,R)-invariant probability measures on the moduli spaces of translation surfaces are regular
• Siegel-Veech transforms are in $L^2$