Density of mild mixing property for vertical flows of Abelian differentials

Abstract

We prove that if g ≥ 2 g\geq 2 , then the set of all Abelian differentials ( M , ω ) (M,\omega ) for which the vertical flow is mildly mixing is dense in every stratum of the moduli space H g \mathcal {H}_g . The proof is based on a sufficient condition due to Frączek, Lemańczyk, and Lesigne guaranteeing mild mixing property of certain special flows over irrational rotations.