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 ${\geqslant}2$ .

Locations

• arXiv (Cornell University) - View - PDF
• Durham Research Online (Durham University) - View - PDF
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• Compositio Mathematica - View