2 problems

Nonnenmacher's finite spectral gap conjecture. There should exist a constant $\gamma>0$ such that every eigenvalue $\tau\neq 0$ satisfies

Let $M$ be a compact hyperbolic surface, let $[\omega]\in H^1(M,\mathbb{C})$ be represented by a harmonic complex-valued $1$-form, and let … For real-valued coefficients of…