Let $M$ be a **closed** Riemannian manifold and $\Delta$ its Laplace-Beltrami operator. Then we have Yau's estimate on the first (non-zero) eigenvalue $\lambda_1>0$ of $\Delta$ acting on functions in terms of bounds on the Ricci curvature, the diameter and the volume of $M$.

**1.** Is there any estimate like this for $\Delta$ acting on forms?

**2.** Is an estimate like this know to be false assuming only Ricci, volume and diameter bounds?

**3.** If we assume a "nice" degeneration of Riemannian manifolds, like K3 surfaces close arising from the Kummer construction degenerating to $T^4/{\bf Z}_2$, can we control first eigenvalue of $\Delta$ on forms (from below) along a degenerating sequence?