On the special Lagrangian spheres near adiabatic limits

Yu-Shen Lin, Boston University
Fine Hall 314

Special Lagrangian submanifolds are an important class of minimal submanifolds in Calabi-Yau manifolds. However, there are not many known examples in compact Calabi-Yau manifolds due to the lack of knowledge of behavior of the Calabi-Yau metric. In this talk, we will explain a construction of special Lagrangian 3-spheres in Calabi-Yau 3-folds with K3-fibration, when the K3 fibres are collapsing. Moreover, these special Lagrangians converge to an interval in the sense of Gromov-Hausdorff under the adiabatic limit. We will also discuss the relation with the Thomas-Yau conjecture. This is a joint work with Shih-Kai Chiu.