On Selberg's Eigenvalue Conjecture for moduli spaces of abelian differentials

Abstract

J.-C. Yoccoz proposed a natural extension of Selberg's Eigenvalue Conjecture to moduli spaces of abelian differentials. We prove an approximation to this conjecture. This gives a qualitative generalization of Selberg's $\frac{3}{16}$ Theorem to moduli spaces of abelian differentials on surfaces of genus $\ge 2$.

49 pages. Added section giving the Dolgopyat-type argument

References in corpus (2)

• Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle
• Classification of Rauzy-Veech groups: proof of the Zorich conjecture

Cited by in corpus (2)

• Counting saddle connections in a homology class modulo $q$
• Fundamental groups and group presentations with bounded relator lengths