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

Density of mild mixing property for vertical flows of Abelian differentials