| Abstract: |
I will discuss an example of complete Calabi-Yau metrics on C^3 with maximal volume growth, which fails to be Euclidean. The construction itself uses the Tian-Yau existence strategy, once an ansatz metric near infinity is prescribed. The motivation comes from collapsing Calabi-Yau metrics on compact 3-folds with a Lefschetz K3 fibration to CP1. It turns out the metric on C^3 is the local model of a tiny region in this global 3-fold, a fact first suggested by nonlinear analysis and then subsequently proved by gluing. |
