Collapsing of Calabi-Yau manifolds and special lagrangian submanifolds

摘要

In this paper, the relationship between the existence of special lagrangiansubmanifolds and the collapsing of Calabi-Yau manifolds is studied. First,special lagrangian fibrations are constructed on some regions of boundedcurvature and sufficiently collapsed in Ricci-flat Calabi-Yau manifolds. Then,in the opposite direction,it is shown that the existence of special lagrangiansubmanifolds with small volume implies the collapsing of some regions in theambient Calabi-Yau manifolds.