Title: A new complete Calabi-Yau metric on $\mathbb{C}^3$,
Abstract: Motivated by the study of collapsing Calabi-Yau threefolds with a Lefschetz
K3 fibration, we construct a complete Calabi-Yau metric on $\mathbb{C}^3$ with
maximal volume growth, which in the appropriate scale is expected to model the
collapsing metric near the nodal point. This new Calabi-Yau metric has singular
tangent cone at infinity, and its Riemannian geometry has certain non-standard
features near the singularity of the tangent cone $\mathbb{C}^2/\mathbb{Z}_2
\times \mathbb{C}$, which are more typical of adiabatic limit problems. The
proof uses an existence result in H-J. Hein's PhD thesis to perturb an
asymptotic approximate solution into an actual solution, and the main
difficulty lies in correcting the slowly decaying error terms.