Rigidity for Multi-Taub-NUT metrics

This paper provides a classification result for gravitational instantons with cubic volume growth and cyclic fundamental group at infinity. It proves that a complete hyperk"ahler manifold asymptotic to a circle fibration over the Euclidean three-space is either the standard ${\text{rl}}^3\times {\text{sph}}^1$ or a multi-Taub-NUT manifold. In particular, the underlying complex manifold is either $\text{cx}\times \text{cx}\mathrm{/}\text{ir}$ or a minimal resolution of a cyclic Kleinian singularity.